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NBER WORKING PAPER SERIES
THE EFFECTS OF DOWNSTREAM COMPETITION ON UPSTREAM INNOVATION AND LICENSING
Jean-Etienne de BettigniesBulat GainullinHua Fang Liu
David T. Robinson
Working Paper 25166http://www.nber.org/papers/w25166
NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue
Cambridge, MA 02138October 2018
We thank Ashish Arora, Luis Cabral, Anne Duchêne, Nancy Gallini, Patrick de Lamirande, Andrea Mantovani, Tom Ross, and seminar participants at the University of Alberta, the 2nd Asia-Pacific Innovation Conference (Singapore, 2011), the EARIE Conference (Rome, 2012), the CEA Meetings (Montreal, 2013), the IIO Conference (Indianapolis, 2018), and the SIOE Conference (Montreal, 2018) for helpful comments. Bettignies gratefully acknowledges financial support from SSHRC. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.
© 2018 by Jean-Etienne de Bettignies, Bulat Gainullin, Hua Fang Liu, and David T. Robinson. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
The Effects of Downstream Competition on Upstream Innovation and Licensing Jean-Etienne de Bettignies, Bulat Gainullin, Hua Fang Liu, and David T. Robinson NBER Working Paper No. 25166October 2018JEL No. L22,L24,O31,O32
ABSTRACT
We study how competition between two downstream firms affects an upstream innovator's innovation strategy, which includes selecting how much innovation to produce and whether to license this innovation to one (targeted licensing) or both (market-wide licensing) downstream competitors. Our model points to a U-shaped relationship between downstream competition and upstream innovation: at low levels of competition, market-wide licensing is optimal and competition reduces innovation, while at high levels of competition targeted licensing is optimal and competition increases innovation. Empirical analysis using a large panel of US data provides clear support for these predictions linking competition, innovation and licensing.
Jean-Etienne de BettigniesSmith School of BusinessQueen's University143 Union StreetKingston, ON, K7L 3N6Canada [email protected]
Bulat GainullinGulf CapitalAbu Dhabi Global Market Square P.O. Box 27522Abu DhabiUnited Arab Emirates [email protected]
Hua Fang LiuSmith School of BusinessQueen's University143 Union StreetKingston, ON K7L 3N6 [email protected]
David T. Robinson Fuqua School of Business Duke University100 Fuqua Drive Durham, NC 27708and [email protected]
1 Introduction
Understanding how competition affects innovation is one of the oldest and most elusive theoretical and
empirical challenges in industrial organization and innovation economics. Schumpeter (1934, 1942)
famously argued that competition weakens incentives to innovate by lowering monopoly rents. In
contrast, Stigler’s (1958) survivor principle argued that competition promotes innovation by weeding
out less innovative, and hence less efficient, firms, and Arrow (1962) suggested that incumbent monop-
olists may have weaker innovation incentives because they internalize the cannibalization of their own
existing products.1 Empirical evidence is equally ambiguous: empirical studies find positive, negative,
or non-monotonic relations between innovation and competition depending on the empirical context.2
This paper offers a new perspective on this question. Our analysis is motivated by the fact that
innovations often take place in markets upstream from those in which the relevant product market
competition occurs. In these settings, intellectual property rights allow for the innovations to be
licensed to downstream firms in technology markets. In the chemical industry, for example, 79% of
technology used is obtained through licensing (Arora and Fosfuri, 2000). We develop and test a model
based on these insights that links competition, technology markets, and innovation.
In particular, we study how downstream competition between two product market rivals impacts an
upstream innovator’s optimal licensing and innovation strategies. The model delivers a non-monotonic,
U-shaped relation between downstream competition and upstream innovation. Our empirical analysis
confirms these predictions. Taken together, the results highlight the subtle connection between com-
petition and innovation across markets that helps to explain the tenuous relationship emerging from
the empirical literature.
We consider a market for technology in which an upstream innovator serves two downstream firms
exogenously located at either end of a Hotelling (1929) line. The innovator makes an investment in a
cost-reducing innovation which, once generated, can be licensed in the downstream market by one of
two means: either the innovation is licensed to a single competitor through “targeted” licensing, or it
is licensed to both competitors at the same time, which we call “market-wide” licensing. The upstream
innovator chooses a licensing strategy and innovation policy to maximize her profits, which in turn
1More recent work has focused on the connection between competition, agency costs, and innovation; suggesting thatcompetition may spur/hinder innovation by mitigating/exacerbating agency problems (Hart, 1983; Scharfstein, 1988;Hermalin, 1992; Schmidt, 1997; Raith, 2003; Baggs and Bettignies, 2007; Bettignies and Ross, 2014).
2Competition has a positive impact on innovation in Geroski (1990), Bertschek (1995) and Blundell et al. (1999); anegative effect in Hashmi (2013), and an inverted-U effect in Aghion et al. (2005). We discuss our relation to Aghion etal. (2005) in more detail below.
1
are a function of the degree of competition in the downstream market. The strategic implications
of the licensing choice are critical: targeted licensing allows a single downstream firm to gain a cost
advantage over its rival, which allows it to steal market share. In contrast, market-wide licensing
allows each downstream firm to avoid facing both cost and demand disadvantages relative to its rival.
In a sense, targeted licensing confers an offensive advantage while market-wide licensing confers a
defensive advantage. We exploit this difference between licensing strategies to derive and explain two
key insights linking competition and innovation.
The first insight links downstream competition to optimal licensing arrangements. First, competi-
tion increases the innovator’s licensing revenue from targeted licensing, but reduces her revenue from
market-wide licensing, thereby unambiguously increasing the relative appeal of targeted licensing to
the innovator. This occurs because competition has two offsetting effects on licensing revenue. On the
one hand, it leads downstream firms to lower their prices and hence their margins. This rent reduction
effect reduces downstream firms’ willingness to pay for the license, and in turn the innovator’s licensing
revenue under both licensing strategies. On the other hand, competition enables a firm with a small
innovation-driven cost advantage to “steal” more business from its rival and to increase demand at
their expense. Under targeted licensing, this business stealing effect increases a sole licensee’s pay-
off, which increases that firm’s willingness to pay for the license and hence the innovator’s licensing
revenue. Under market-wide licensing, business stealing increases both firms’ willingness to pay by
decreasing the payoff that they would obtain if they did not purchase the license while the other firm
did. Thus business stealing increases licensing revenue under both licensing strategies.
The distinct effects of competition on licensing revenue across licensing strategies come from the
differential strength of the business stealing effect. Under targeted licensing, business stealing effect
is strong. Competition increases the demand advantage of the licensed firm, and this increase in
demand has large effect on that firm’s payoff because as mentioned above that firm - having gained
a cost advantage over its rival - enjoys a large markup. In this case business stealing dominates rent
reduction, and the net impact of competition on the licensing candidate’s willingness to pay for the
license is positive. In contrast, under market-wide licensing, business stealing is weak. Competition
exacerbates the demand disadvantage each firm would have if it did not purchase the license while its
rival did, but the impact of this decrease in demand on the firm’s payoff is small because the firm with
a cost disadvantage relative to its rival would enjoy a smaller markup. Thus, in that case, business
stealing is dominated by rent reduction, and the net impact of competition on the licensing candidate’s
2
willingness to pay for the license is negative.
The second key insight of the model concerns the impact of downstream competition on the
upstream innovator’s incentives to innovate, which differs across licensing strategies. Competition
affects the innovator’s marginal benefit from innovation through business stealing and rent reduction
effects in a similar manner to that described above. Larger demands and markups under targeted
licensing generate a strong business stealing effect, strong enough to offset rent reduction and to
yield a positive effect of competition on innovation. In contrast, lower demands and markups under
market-wide licensing generate a weak business stealing effect and a negative impact of competition
on innovation.
Taken together, these insights show that the relationship between downstream competition and
upstream innovation is inextricably connected to the innovator’s licensing strategy. Indeed, we show
that a threshold level of downstream competition may exist such that below this threshold market-wide
licensing is optimal and innovation decreases with competition; while above the threshold targeted
licensing is optimal and innovation increases with competition. In sum, the model predicts a non-
monotonic, U-shaped relation between downstream competition and upstream innovation, with a
switch-point driven by licensing considerations.
The second part of our analysis tests two key predictions from our model using a large panel of
publicly traded U.S. firms over the period 1976 − 2006. The first prediction regards the U-shaped
relation between downstream competition and upstream innovation. Simple descriptive tests linking
patenting activity to a downstream industry’s Lerner index clearly reveal a U-shaped relationship
between downstream competition and upstream innovation. But tests of this nature are fraught with
endogeneity concerns, because future profitability in an industry affects both the incentive to innovate
as well as the incentives for challengers to enter the market. To address these, we use the reductions in
import tariff rates as an exogenous shock to the competitive structure of an industry. The key to our
identification strategy rests in the fact that firms in industries with large reductions in import tariff
rates face higher competition, but the reduction of import tariffs has no direct impact on the optimal
choice of licensing strategies except through the change in downstream demand conditions.
Overall our identification strategy supports the idea that downstream competition has a non-linear
causal impact on upstream innovation. Regardless of whether we model the threshold analytically or
simply split the data at the median level of competitiveness, we find that innovation decreases with
competition below the threshold and increases with competition above it.
3
The second piece of our empirical analysis implicates licensing choices as a key channel behind
the U-shaped relation. Consistent with the theoretical model, data on strategic alliance and licens-
ing deals illustrates that downstream competition increases the appeal of targeted licensing relative
to market-wide licensing; and upstream innovation increases (decreases) in downstream competition
under targeted (market-wide) licensing.
Perhaps closest to our paper is Aghion et al.’s (2005) work, which identifies an inverted-U relation-
ship between competition and innovation. In a way, the U-shaped relationship between downstream
competition and upstream innovation predicted by our model is the opposite of the relationship de-
rived in Aghion et al. (2005). Although both analyses model innovation as a cost-reducing process,
the critical difference lies in the fact that Aghion et al. (2005) study the connection between product
market competition and innovation within a given industry, whereas in our analysis, competitors in a
downstream market are effectively renting the right to use an external innovation on terms that are
dictated by the upstream innovator. Our rent-reduction and business stealing effects of competition
are similar to their Schumpeterian and escape-competition effects in their model, although they emerge
explicitly from the strategic interactions between downstream competitors in our framework.
Our work is also related to the literature on “outsider patentee” licensing, which considers an
innovation undertaken by an upstream innovator who then licenses the innovation to firms competing
in the downstream product market,3 and to the “insider patentee” licensing literature which exam-
ines the voluntary transfer of technology/innovation from one downstream competitor to another.4
In particular, Fauli-Oller et al. (2011) suggests that mergers in the downstream market (and the
concomitant reduction in competition) should be associated with increased R&D investments by the
upstream innovator supplying all of the downstream competitors.5 We depart from these lines of
work by endogenizing both innovation decisions and licensing decisions. This allows us to unpack the
specific, simultaneous and related effects of competition on licensing and innovation strategies.
The balance of the paper proceeds as follows. In Section 2, we set up the basic model and derive
3See Kamien and Tauman (1984, 1986) Katz and Shapiro (1986), Muto (1993), Schmitz (2002), Poddar and Sinha(2004), Bagchi (2008), Farrell and Shapiro (2008), Allain et al. (2011), Fauli-Oller et al. (2011), Fauli-Oller and Sandonis(2012), and Chatain (2014).
4See Gallini (1984), Gallini and Winter (1985), Katz and Shapiro (1987), Fauli-Oller and Sandonis (2002), Arora andFosfuri (2003), and Erkal (2005).
5See also the recent work of Chatain (2014), which examines the “the interplay between product market, strategicfactor market, and resource development” in a framework that could be interpreted as one of outsider patentee licensing;and in that sense addresses a research question similar to ours. Our approach departs from his in our use of a locationmodel of competition (in contrast to his reduced-form approach to modeling competition) to place strategic interactionin the downstream product market at the forefront of the analysis; and in our endogenizing of both innovation andlicensing decisions.
4
equilibrium outcomes under market-wide and targeted licensing. Section 3 analyzes the effects of
competition on the innovator’s optimal licensing and innovation strategies. In Section 4, we introduce
the data required to test the model, while in Section 5, we present the main empirical findings. Finally,
Section 6 concludes. The proofs of Lemmas 1 and 2, and of Proposition 2, are in the appendix; all
other proofs follow directly from the text.
2 Basic Model
2.1 Setup
The setup of the model can be described as follows:
Firms and Consumer. Two firms, 1 and 2, are positioned at each end of a Hotelling (1929) line,
with locations x1 = 0 and x2 = 1, respectively. The two firms face marginal costs c1 = c2 = c, and
compete in price p.
Without loss of generality we posit that a unique consumer, whose location is random and uniformly
distributed along the line, purchases one unit of the product from either Firm 1 or Firm 2. Firms 1
and 2 know the distribution of the location of the consumer, but they do not know the actual location
on the line. At location x, the consumer incurs a transport cost tx for travelling to Firm 1 and a
cost t (1− x) to visit Firm 2. The consumer enjoys conditional indirect utility U1 = s− p1 − tx from
product 1 and U2 = s − p2 − t (1− x) from product 2 (where s represents income), and selects the
utility-maximizing product. The resulting expected demand for Firm i, i = 1, 2, is:
di (pi, pj , t) =1
2+
(pj − pi)2t
. (1)
Product Market Competition. The “Hotelling” parameterization of competition is a natural
choice here, for two main reasons. First, given our ultimate purpose - comparative statics on the degree
of competition - the transport cost t, which measures the degree of horizontal product differentiation,
or rather its inverse θ = 1/t which captures the degree of homogeneity between products, is an ideal
parameter to represent what Sutton (1992, p.9) defined in his classic work as toughness of competition.
Second, the Hotelling model is the simplest and most tractable framework to work with, relative to
other candidate modeling choices, and indeed offers general insights at the lowest analytical cost.
Thus, as is common in the industrial organization literature, throughout the paper we use the degree
5
of substitutability between products, θ, as our measure of competition. We restrict our attention to
value of θ ∈ Θ with Θ ≡ (0, 9/2), which ensures strict concavity of all maximization programs as well
as positive equilibrium prices, demands and profits (see proofs of Lemmas 1 and 2).6
Innovation. Upstream from the two product market competitors, an innovator is working on an
innovation that can be licensed to the downstream firms. For simplicity and concreteness, we refer to
this as a cost-reducing innovation, but a value-enhancing innovation works same here as it also leads
to quality improvement of downstream firms’ products. The innovator has two alternatives. Under
targeted licensing, she chooses innovation level ∆T and licenses it to Firm 1 only. We assume the
innovator can commit to license to only one firm under targeted licensing; for example by making
the innovation specific to that one firm, or contractually granting exclusive use of the innovation to
that one firm.7 Under market-wide licensing, she chooses innovation level ∆M and licenses it to both
firms 1 and 2. An innovation ∆ benefits the licensees by reducing their marginal cost of production
by ∆; and costs the innovator KT (∆) = ∆2/2 under targeted licensing and KM (∆) = ∆2/2 +h, with
h ∈ R+, under market-wide licensing. Parameter h captures all additional transaction costs associated
with negotiating the second license under market-wide licensing.
Contracts. We assume that downstream rivals’ profits and output cannot be verified by third
parties such as courts, and are thus not contractible. This could arise for example if downstream
managers can spend cash flows on “perks” which “may be difficult to distinguish from appropriate
business decisions [...]” (Bolton and Scharfstein, 1996). This contractual incompleteness rules out
two-part tariffs (fixed fee plus royalty) - which are based on profits or output measures - as possible
licensing frameworks. We also assume that transaction costs associated with setting up auctions are
prohibitively high, making auctions difficult to implement. Accordingly throughout the main text we
focus on fixed fees as the licensing contracts between the innovator and downstream firms. This is
not an unrealistic assumption. In the chemical industry for instance, contracts usually include fixed
fees. While some innovators may set royalties on output, determined by industry norms at around
2%, others, like SEFs for instance, “tend to favor lump sum payments, unwilling or unable to track
how the project does after commissioning” (Arora and Fosfuri, 2000). In Appendix C we also consider
6In setting this type of simplifying parametric restriction we follow Raith (2003) and others.7Commitment is important here. As is well-known from the foreclosure literature, the innovator may have an incentive
to sell a license to the second downstream firm after having sold a license to the first one. Anticipating this, the firstlicensee would have a lower willingness to pay for the license in the first place. See e.g. Rey and Tirole’s (2007) reviewof the foreclosure literature.
6
licensing contracts based on auctions, and on two-part tariffs; and show that qualitatively similar
results continue to hold.
Thus, we assume that under market-wide licensing innovation ∆M is licensed to firms 1 and 2,
respectively, for license fees z1M and z2M ; and that under targeted licensing, innovation ∆T is licensed
to Firm 1 for license fee z1T .
Timing of the Game. At date 0, the innovator chooses between market-wide licensing and
targeted licensing. At date 1, under market-wide licensing, the innovator selects {∆M , zM1, zM2}; and
under targeted licensing she selects {∆T , z1T }. At date 2, firms offered a license decide whether or not
to purchase it, taking the license fee as given. Marginal costs of production are determined. At date
3, after observing each other’s marginal costs, firms 1 and 2 compete in price. Demands and profits
are realized.
2.2 Market-Wide Licensing
Suppose the innovator plans to license innovations to both downstream firms. We derive the equilib-
rium by backward induction.
At date 3, price competition takes place between firms 1 and 2. Specifically, Firm i, i = 1, 2,
chooses pi to maximize its expected payoff, taking costs and innovations as given:
maxpiπi (∆i, pi, pj , θ) = max
pi(pi − c+ ∆M ) di (pi, pj , θ) , (2)
with expected demand di (pi, pj , θ) defined as in (1). Taking the first-order conditions (FOCs) with
respect to price for i = 1, 2 and solving the resulting system of two equations yields the following
equilibrium price-cost margin Pi:
Pi = pi − c+ ∆i =1
θ+
∆i −∆j
3. (3)
Substituting equilibrium prices back into the expected demand, we obtain an expression for expected
profits as a function of innovations:
πi (∆i,∆j , θ) = Pi (∆i,∆j , θ) di (∆i,∆j , θ) =
[1
θ+
∆i −∆j
3
] [1
2+
(∆i −∆j) θ
6
], (4)
7
where di =[
12 +
(∆i−∆j)θ6
]is the expected demand for Firm i. Under market-wide licensing, of course,
∆i = ∆j = ∆M , and Firm i’s expected profits simplify to πi (∆iM ,∆jM , θ) = 1/ (2θ).
At date 2, as can readily be shown, in equilibrium Firm i licenses innovation ∆M from the innovator
if and only if (iff) the payoff it can obtain if it buys the license is at least as large as its payoff if it
does not buy the license: πi (∆i,∆j , θ)− ziM (∆i,∆j , θ) ≥ πi (0,∆j , θ), with ∆i = ∆j = ∆M .
At date 1, the foresighted innovator sets the highest license fee ziM that she can extract from Firm
i, subject to both firms buying the license, which is simply:
ziM (∆M , θ) = πi (∆M ,∆M , θ)− πi (0,∆M , θ) =1
2θ−[
1
θ− ∆M
3
] [1
2− ∆Mθ
6
]. (5)
Under market-wide licensing, Firm i takes as given that Firm j has access to innovation ∆M . The
optimal license fee to charge Firm i - which is Firm i’s willingness to pay for the license - is the difference
between Firm i’s profits if it obtains access to innovation ∆M -“symmetric profits” πi (∆M ,∆M , θ),
since in this case both rivals have access to the same innovation - and its profits without access to the
innovation -“laggard profits” πi (0,∆M , θ), since in that case Firm i has no access to the innovation
while Firm j does.8 The innovator chooses innovation ∆∗M to maximize the following payoff:
ZM = z1M (∆M , θ) + z2M (∆M , θ)−KM (∆M ) . (6)
Using expression (6), and taking the FOC with respect to ∆M , yields ∆∗M such that:
− ∂π1
∂∆2(0,∆∗M , θ)−
∂π2
∂∆1(0,∆∗M , θ) =
∂K
∂∆M(∆∗M ) . (7)
Clearly, a marginal increase in innovation ∆M has no impact on symmetric profits: ∂πi∂∆M
(∆M ,∆M , θ) =
∂(1/2θ)∂∆M
= 0. This is because an increase in ∆M identically lowers the marginal costs of both firms, and
these identical changes in marginal costs neutralize each other in the profit function.
In contrast, a marginal increase in innovation ∆M does reduce laggard profits for firms 1 and 2.
An increase in ∆M reduces the profits that Firm 1 (resp. 2) makes if it does not license the innovation,
8This is a so-called “offer game,” in which the principal (innovator) makes simultaneous offers to the agents (down-stream firms), examined by Segal (1999, 2003), Genicot and Ray (2006), and more recently Galasso (2008), among others.Equation (C.3) defines the cheapest way for the principal to ensure “acceptance” by agents, i.e. to have (accept, accept)as a Nash equilibrium. In principle, even if (C.3) holds, (reject, reject) may also be an equilibrium. Segal (1999) simplyrules this equilibrium out by assuming that the principal can coordinate agents on his preferred equilibrium. We do notneed this assumption here, as one can readily verifiy that - in our Hotelling framework, at the equilibrium innovation level∆∗M = 6
9+2θ- we have πi (∆∗M , 0, θ)−[πi (∆∗M ,∆
∗M , θ) − πi (0,∆∗M , θ)] > πi (0, 0, θ), for i = 1, 2, ruling out (reject, reject)
as an equilibrium.
8
because it increases the cost disadvantage Firm 1 would have relative to a licensed Firm 2 (resp. 1) in
that case. By decreasing Firm 1’s and Firm 2’s laggard profits, an increase in ∆M raises these firms’
willingness to pay to license the innovation in order to avoid this laggard situation. These marginal
effects on the firms’ willingness to pay and hence on the innovator’s licensing revenue are depicted on
the left-hand side of (7). The right-hand side represents the innovator’s marginal cost of innovating.
As shown in Appendix B, solving the FOC for ∆∗M yields a unique equilibrium:
Lemma 1 Under market-wide licensing, a unique equilibrium exists, in which the innovator chooses
innovation levels ∆∗M = 69+2θ . This in turn implies downstream price-cost margins P1 (∆∗M ,∆
∗M , θ) =
P2 (∆∗M ,∆∗M , θ) = 1/θ; and expected demands d1 (∆∗M ,∆
∗M , θ) = d2 (∆∗M ,∆
∗M , θ) = 1/2. License fees,
and payoff to the innovator, simplify to z1M = z2M = 2(9+θ)
(9+2θ)2 , and Z∗M = 2(9+2θ) − h, respectively.
2.3 Targeted Licensing
Suppose now that the innovator plans to license her innovation to Firm 1 only. Then:
At date 3, given that the innovator has licensed innovation ∆T to Firm 1 but not to Firm 2, price
competition is the same as in Section 2.2, and profits for firms 1 and 2 can be expressed using (4) as
π1 (∆T , 0, θ) and π2 (0,∆T , θ), respectively.
At date 2, in equilibrium Firm 1 licenses innovation ∆T from the innovator iff the payoff it can
obtain if it buys the license is at least as large as its payoff if it does not buy the license: π1 (∆T , 0, θ)−
z12 (∆T , 0, θ) ≥ π1 (0, 0, θ).
At date 1, the foresighted innovator sets the highest license fee zT that she can extract from Firm
1, which is simply:
z1T (∆T , θ) = π1 (∆T , 0, θ)− π1 (0, 0, θ) =
[1
θ+
∆T
3
] [1
2+
∆T θ
6
]− 1
2θ. (8)
Under targeted licensing, Firm 1 takes as given that Firm 2 does not have access to innovation ∆T .
The optimal license fee to charge Firm 1 - Firm 1’s willingness to pay for the license - is the difference
between its profits if it obtains access to innovation ∆T - “leader profits” πi (∆T , 0, θ), since in this
case Firm 1 has access to the innovation while Firm 2 does not - and its profits without access
to the innovation - “symmetric profits” πi (0, 0, θ), since in that case neither firm has access to the
innovation.9
9Alternatively, we could assume that in the event Firm 1 does not gain access to the innovation, Firm 2 would do so.This alternative setup is examined in the Auction Scenario in Appendix C, where similar results are shown to arise.
9
The innovator chooses innovation ∆∗T to maximize the following payoff:
ZT = z1T (∆T , θ)−KT (∆T ) . (9)
Using expression (9), and taking the FOC with respect to ∆T , yields ∆∗T such that:10
∂π1
∂∆1(∆∗T , 0, θ) =
∂KT
∂∆T(∆∗T ) . (10)
Under targeted licensing, the innovator’s marginal benefit from innovation ∆T works by increasing
Firm 1’s innovation advantage if it does obtain access to the innovation, thus increasing Firm 1’s leader
profits. This in turn increases Firm 1’s willingness to pay for the innovation, and the innovator’s
equilibrium licensing revenue. As shown in Appendix B, solving the FOCs for ∆∗T , one obtains a
unique equilibrium:
Lemma 2 Under targeted licensing, a unique equilibrium exists, in which the innovator chooses inno-
vation level ∆∗T = 39−θ . This in turn implies downstream price-cost margins P1 (∆∗T , 0, θ) =
[1θ +
∆∗T3
]and P2 (0,∆∗T , θ) =
[1θ −
∆∗T3
]; and expected demands d1 (∆∗T , 0, θ) =
[12 +
θ∆∗T6
]and d2 (0,∆∗T , θ) =[
12 −
θ∆∗T6
]. License fees, and payoff to the innovator, simplify to z∗1T = 18−θ
2(9−θ)2 , and Z∗T = 118−2θ ,
respectively.
Note that here intra-industry differential firm performance emerges endogenously, similar to Zott
(2003): expected profits are greater for Firm 1 than for Firm 2. While in Zott’s work this differential
arises from differences in the timing, cost, and learning of resource development, here we emphasize
the market for technology and the upstream innovator’s licensing strategy generating this differential.
3 Competition, Licensing and Innovation
The foregoing analysis suggests a key difference between the two types of licensing. On the one hand,
targeted licensing allows one downstream firm to gain a cost advantage over its rival, and thus to
benefit from strong demand and a large markup. On the other hand, market-wide licensing allows
each downstream firm to avoid facing a cost disadvantage relative to its rival, a situation which would
yield weak demand and a small markup. This in turn helps explain the key results of the paper, which
we present below.
10Note that ∆T has no impact on firm 1’s no-access profits: ∂π1 (0, 0, θ) /∂∆T = 0.
10
3.1 Optimal Licensing Strategy
A key difference between the two licensing strategies concerns the way in which competition affects
the innovator’s licensing payoffs. Indeed, as is evident from Lemmas 1 and 2:
Proposition 1 The innovator’s equilibrium payoff under market-wide licensing, Z∗M = 2(9+2θ) − h, is
strictly decreasing in competition. In contrast, the equilibrium payoff under targeted licensing, Z∗T =
118−2θ , is strictly increasing in competition. Thus competition unambiguously increases the appeal of
targeted licensing relative to market-wide licensing.
To see the intuition behind these results, consider the impact of competition on the market-wide
licensing payoff Z∗M and on the targeted licensing payoff Z∗T , respectively:1112
∂Z∗M∂θ
=2∑i=1
∂ziM (∆M , θ)
∂θ=
2∑i=1
∂ [πi (∆M ,∆M , θ)− πi (0,∆M , θ)]
∂θ(11)
=
2∑i=1
[∂Pi (∆M ,∆M , θ)
∂θdi (∆M ,∆M , θ)−
∂Pi (0,∆M , θ)
∂θdi (0,∆M , θ)
]
+
2∑i=1
[−∂di (0,∆M , θ)
∂θPi (0,∆M , θ)
]
and:
∂Z∗T∂θ
=∂z∗T (∆T , θ)
∂θ=∂ [π1 (∆T , 0, θ)− π1 (0, 0, θ)]
∂θ
=
[∂P1 (∆T , 0, θ)
∂θd1 (∆T , 0, θ)−
∂P1 (0, 0, θ)
∂θd1 (0, 0, θ)
](12)
+
[∂d1 (∆T , 0, θ)
∂θP1 (∆T , 0, θ)
].
Competition affects the innovator’s licensing payoffs in two primary ways. First, it induces firms
to lower their prices: using expression (4), one can see that regardless of the values of ∆i and ∆j ,
∂Pi (∆i,∆j , θ) /∂θ = −1/θ2 < 0. This is the rent reduction effect of competition. The first square
bracket in (11) and (12) captures the impact of rent reduction on the licensor’s payoff. Consider market-
wide licensing, for example. It follows directly from above that the negative impact of competition on a
downstream firm’s price-cost margins is independent of whether that firm has access to the innovation
11From the envelope theorem, we know that the impact of competition on the licensor’s payoff that occurs throughchanges in innovation levels is null in equilibrium. Moreover, competition has no impact on equilibrium demand whenfirms have symmetric costs: ∂di (∆,∆, θ) /∂θ = 0.
12For a discussion of the effects of product market competition on profit differentials in the context of entrepreneurialfinance, see Bettignies and Duchene (2015).
11
or not: ∂Pi (∆M ,∆M , θ) /∂θ = −1/θ2 = ∂Pi (0,∆M , θ) /∂θ. However, the overall impact on the firm’s
symmetric profits is more negative than on its laggard profits, because in the former case the decrease
in margin affects a larger equilibrium demand: di (∆M ,∆M , θ) = 1/2 > 1/2− θ∆M/6 = di (0,∆M , θ).
Overall, the impact of rent reduction on the firm’s willingness to pay for the license and on the
innovator’s payoff is −∆M/ (6θ). Similarly, under targeted licensing, the impact of rent reduction on
the innovator’s payoff is −∆T / (6θ).13
The second key effect of competition on the innovator’s licensing payoff is to increase (resp. de-
crease) demand for the firm with a cost advantage (resp. disadvantage): ∂di∂θ =
(∆i−∆j)6 ≷ 0 iff
∆i ≷ ∆j , and ∂di∂θ = 0 iff ∆i = ∆j . This is the business stealing effect of competition. The sec-
ond square bracket in (11) and (12) captures the impact of business stealing on the licensor’s payoff.
Consider market-wide licensing again. The positive (resp. negative) effect of competition on demand
for firms with an innovation advantage (resp. disadvantage) relative to their rivals has no impact on
a downstream firm’s symmetric profits, since in that case ∆∗1M = ∆∗2M . But in the case of laggard
profits, the firm is at an innovation disadvantage relative to its rival, which translates into a demand
disadvantage. Competition exacerbates this disadvantage by reducing demand for that firm. Accord-
ingly, by worsening the firm’s laggard profits, business stealing increases the firm’s willingness to pay
for the license, and the innovator’s payoff by −∂di(0,∆M ,θ)∂θ Pi (0,∆M , θ) = ∆∗M/ (6θ)− (∆∗M )2 /18 > 0.
Under targeted licensing, access to the innovation gives Firm 1 an innovation advantage over Firm 2,
which translates into leader profits. Competition augments this advantage by increasing demand for
that firm. This in turn raises Firm 1’s willingness to pay for the license, and the innovator’s payoff,
by ∂d1(∆T ,0,θ)∂θ P1 (∆T , 0, θ) = ∆T / (6θ) + (∆T )2 /18 > 0.
Clearly, under market-wide licensing the impact of rent reduction dominates the impact of business
stealing, and competition strictly decreases the innovator’s licensing payoff; while in contrast under
targeted licensing the impact of business stealing dominates, and competition strictly increases the
innovator’s licensing payoff. Indeed, competition increases the appeal of targeted licensing relative to
market-wide licensing for the innovator.
This difference in effects of competition on licensing payoff comes primarily from business stealing.
Under market-wide licensing, business stealing increases a firm’s willingness to pay by worsening
demand if the license is not purchased, a situation in which the firm is at an innovation disadvantage
13The intuition is the same as under market-wide licensing. Competition puts downward pressure on price-cost margins,in both leader and symmetric cases; but the overall impact is more negative on leader profits than on symmetric profits,because in the former case the decrease in margin affects a larger equilibrium demand. Hence the negative impact ofrent reduction on willingness to pay for the license.
12
and hence makes relatively small margins. Thus the negative impact of decreased demand on the
licensee’s laggard profits, and the resulting positive effect on his willingness to pay for the license, is
relatively small, too small in fact to offset the negative impact of rent reduction on his willingness
to pay. In contrast under targeted licensing, business stealing works by increasing the firm’s demand
and profits if the license is purchased, a situation in which the firm is at an innovation advantage
and hence makes relatively large margins. Accordingly the positive impact of increased demand on
the firm’s leader profits, and hence on its willingness to pay for the license, is relatively large, large
enough to offset the negative impact of rent reduction.
The innovator’s optimal licensing strategy then follows directly from the preceding analysis. To see
this, recall from Lemmas 1 and 2 that Z∗M = 2(9+2θ) − h and Z∗T = 1
18−2θ for all θ ∈ Θ. It then follows
that limθ→0
Z∗T − Z∗M = −1/6 + h and that limθ→9/2
Z∗T − Z∗M = h; and together with Proposition 1 this
immediately yields the following result regarding the impact of competition on equilibrium licensing
strategy:14
Proposition 2 If the exogenous (relative) cost of market-wide licensing h is low to moderate - h ∈
(0, 1/6) - there exists a threshold level of competition θ∗ (h) ∈ Θ, with ∂θ∗ (h) /∂h < 0, such that the
innovator chooses market-wide licensing for all θ ∈ (0, θ∗ (h)), and chooses targeted licensing for all
θ ∈ [θ∗, 9/2). If h is high - h ≥ 1/6 - targeted licensing is the optimal choice for the innovator for all
θ ∈ Θ.
[Insert Figure 1 here.]
Thus, while competition unambiguously increases the appeal of targeted licensing relative to
market-wide licensing (Proposition 1), as stated in Proposition 2 and depicted in Figure 1 this may
or may not lead to a switch in licensing strategy, depending on the value of the exogenous cost h.
Our view is that in practice, while the additional transaction costs associated with market-wide
licensing do exist, they are not so great as to eliminate this licensing strategy as an optimal choice
regardless of the degree of competition. Accordingly, our prediction is that competition will have an
impact on the innovator’s licensing strategy, leading to a switch from market-wide licensing to targeted
licensing. We test this prediction empirically in Sections 4 and 5.
14Some further thoughts on this licensing tradeoff, and how it is affected by downstream competition, are presentedin Appendix C.
13
Note from Proposition 2 that the threshold level of competition θ∗ (h) at which the innovator
switches from market-wide licensing to targeted licensing is strictly decreasing in the exogenous cost
of market-wide licensing: ∂θ∗ (h) /∂h < 0. Intuitively, the greater the cost of market-wide licensing,
the “sooner” the innovator will switch to targeted licensing at competition intensifies.
Also note that our result that downstream competition (measured by the degree of substitutability
between products) may lead the upstream innovator to reduce the number of licenses is consistent with
Bagchi (2008), which illustrates a similar result albeit in a different context of licensing auctions and
differentiated downstream Cournot markets. What is more novel here is our use of this result to im-
prove our understanding of the interaction between downstream competition and upstream innovation.
This is the purpose of our analysis below.
3.2 Optimal Innovation Strategy
3.2.1 Licensing and Innovation
A key difference between the two licensing strategies concerns the way in which competition affects
equilibrium innovation. Indeed, it is immediately clear from lemmas 1 and 2 that:15
Proposition 3 Equilibrium innovation under market-wide licensing, ∆∗M = 69+2θ , is strictly decreas-
ing in competition. In contrast, equilibrium innovation under targeted licensing, ∆∗T = 39−θ , is strictly
increasing in competition. Moreover, there exists a threshold level of competition θ∗∗ = 9/4 such that
∆∗T < ∆∗M for all θ ∈ (0, θ∗∗) and ∆∗T ≥ ∆∗M for all θ ∈ [θ∗∗, 9/2).
To understand the intuition behind these results, let us first use (5) and (7), and (8) and (10),
to derive the marginal impact of innovation on the innovator’s licensing revenue, under market-wide
licensing and targeted licensing, respectively:
2∑i=1
∂ziM (∆M , θ)
∂∆M=
2∑i=1
[− ∂πi∂∆j
(0,∆M , θ)
](13)
=2∑i=1
[− ∂di∂∆j
(θ)Pi (0,∆M , θ)−∂Pi∂∆j
di (0,∆M , θ)
]
=
2∑i=1
[θ
6Pi (0,∆M , θ) +
1
3di (0,∆M , θ)
],
15The threshold value θ∗∗ = 9/4 is obtained simply by solving ∆∗M = 69+2θ
= 39−θ = ∆∗T for θ.
14
and:
∂z1T (∆T , θ)
∂∆T=
∂π1
∂∆1(∆T , 0, θ) (14)
=∂d1
∂∆1(θ)P1 (∆T , 0, θ) +
∂P1
∂∆1d1 (∆T , 0, θ)
=θ
6P1 (∆T , 0, θ) +
1
3d1 (∆T , 0, θ) .
Consider the innovator’s market-wide licensing revenue from Firm i. Increasing innovation ∆M
increases Firm i’s willingness to pay for the innovation by increasing the cost advantage that its rival
Firm j will have if Firm i does not license the innovation - in other words it decreases Firm i’s
laggard profits. It does so in two ways. First, the increase in Firm j’s cost advantage enables that
firm to steal market share at the expense of Firm i:∂dj∂∆j
(θ) = θ6 > 0 and ∂di
∂∆j(θ) = − θ
6 < 0; and
the impact on Firm i’s laggard profits is the margin-adjusted marginal change in expected demand,
∂di∂∆j
(θ)Pi (0,∆M , θ) < 0. Second, the increase in Firm j’s cost advantage enables that firm to increase
its price-cost margin in equilibrium, and forces a smaller price-cost margin (through lower equilibrium
price) onto Firm i:∂Pj∂∆j
= 13 > 0 and ∂Pi
∂∆j= −1
3 < 0; and the impact on Firm i’s laggard profits is the
demand-adjusted marginal change in price-cost margin, ∂Pi∂∆j
di (0,∆M , θ) < 0.
Next, consider targeted licensing revenue from Firm 1. Here in contrast, increasing innovation
∆T increases Firm 1’s willingness to pay for the innovation by increasing the cost advantage that it
will have over Firm 2 if it does license the innovation - in other words it increases Firm 1’s leader
profits. Again, this works in two ways. First, the increase in Firm 1’s cost advantage enables that
firm to steal market share from Firm 2 ( ∂d1∂∆1
(θ) = θ6 > 0); increasing Firm 1’s leader profits by
∂d1∂∆1
(θ)P1 (∆T , 0, θ) > 0. Second, the increase in Firm 1’s cost advantage leads to a higher price-cost
margin for that firm ( ∂P1∂∆1
= 13 > 0); increasing Firm 1’s leader profits by ∂P1
∂∆1d1 (∆T , 0, θ) > 0.
Now, differentiating (13) and (14) with respect to θ, we derive the effects of competition on
the innovator’s marginal benefit (in terms of licensing revenue) from innovation, under market-wide
licensing and targeted licensing, respectively:
2∑i=1
∂
[−∂πi (0,∆M , θ)
∂∆j
]/∂θ =
2∑i=1
∂di(0,∆M ,θ)∂θ
[− ∂Pi∂∆j
]+ ∂Pi(0,∆M ,θ)
∂θ
[− ∂di∂∆j
]+[− ∂2di∂∆j∂θ
]Pi (0,∆M , θ)
, (15)
15
and:
∂
[∂π1 (∆T , 0, θ)
∂∆1
]/∂θ =
∂d1 (∆T , 0, θ)
∂θ
[∂P1
∂∆1
]+∂P1 (∆T , 0, θ)
∂θ
[∂d1
∂∆1
]+
∂2d1
∂∆1∂θP1 (∆T , 0, θ) . (16)
The degree of competition θ - by making consumers more sensitive to prices relative to their
position on the Hotelling line - has three effects on the marginal impact of innovation on licensing
revenue.16 As shall now become clear, the forces at work are very similar to the ones shown above to
affect licensing revenues.
The first factor in (15) and (16) captures the business stealing effect of competition on the marginal
licensing revenue from innovation. Consider market-wide licensing: by reducing laggard demand for
Firm 1, this effect mitigates the reduction in Firm 1’s laggard profits resulting from the drop in
price-cost margin associated with an increase in innovation ∆M in Firm 2. It therefore mutes Firm
1’s increased willingness to pay for the license and reduces the innovator’s marginal benefit from
innovation.17 In contrast, under targeted licensing, by increasing leader demand for Firm 1, this effect
amplifies the increase in leader profits resulting from the increase price-cost margin associated with
an increase in innovation ∆M in Firm 1. Thus under targeted licensing this exacerbates Firm 1’s
increased willingness to pay and increases the innovator’s marginal benefit from innovation.
The second factor in (15) and (16) captures the rent reduction effect of competition on the marginal
licensing revenue from innovation. Under market-wide licensing, the price reduction associated with
more intense competition mitigates the reduction in Firm 1’s laggard profits resulting from the drop
in laggard demand associated with an increase in innovation ∆M in Firm 2. It therefore mutes Firm
1’s increased willingness to pay for the license. Under targeted licensing, the price reduction mitigates
the increase in Firm 1’s leader profits resulting from the increase in leader demand associated with an
increase in innovation ∆T , thus dampening Firm 1’s increased willingness to pay. Thus under both
licensing strategies, this effect reduces the marginal benefit from innovation.
The third factor in (15) and (16) captures an effect we have not discussed yet: the increased
business stealing effect of competition (Baggs and Bettignies, 2007), which has a positive impact on
the marginal product of innovation.18 Under market-wide licensing, this effect exacerbates the decrease
16Note from above that ∂Pi∂∆i
= 13
and ∂Pi∂∆j
= − 13
are independent of competition θ, and hence ∂2Pi∂∆j∂θ
= ∂2Pi∂∆i∂θ
= 0.17This effect is related to what Gosh et al. (2015) call “share-reduction effect” in the context of continuous improvement
versus discrete innovation.18While the direct business stealing effect of competition affects the levels of demand associated with given levels of
innovation, in contrast the increased business stealing effect of competition affects the changes in demand associatedwith an innovation increase
16
in Firm i’s laggard demand - and hence exacerbates Firm i’s increased willingness to pay for a license
- associated with an increase in innovation ∆M . Under targeted licensing, this effect amplifies the
increase in Firm 1’s leader demand associated with an increase in ∆T , hence magnifying its increased
willingness to pay for the license. Accordingly, under both licensing strategies, this effect increases the
innovator’s marginal benefit from innovation.
Using (4) to determine the magnitude of each of these effects, one can easily verify that the
differential effects of competition on innovation across licensing strategies comes primarily from dif-
ferences in increased business stealing. Under market-wide licensing, the impact of increased busi-
ness stealing simplifies to[− ∂2di∂∆j∂θ
]Pi (0,∆M , θ) = 1/ (6θ) − ∆M/18 > 0. This effect is relatively
weak, in the sense that it fails to outweigh the negative impact of rent reduction, which simplifies
to ∂Pi(0,∆M ,θ)∂θ
[− ∂di∂∆j
]= −1/ (6θ) < 0. Together these two effects imply a negative impact of com-
petition on the marginal benefit from innovation; and the business stealing effect, which simplifies
to ∂di(0,∆M ,θ)∂θ
[− ∂Pi∂∆j
]= −∆M/18 < 0, exacerbates this negative impact. Thus, under market-wide
competition decreases the innovator’s marginal benefit from innovating, thereby reducing equilibrium
innovation ∆∗M .
In contrast, under targeted licensing, the impact of increased business stealing can be shown to
simplify to ∂2d1∂∆1∂θ
P1 (∆T , 0, θ) = 1/ (6θ) + ∆T /18 > 0. It is relatively strong in that is does out-
weigh the negative impact of rent reduction (which itself is the same under both licensing strate-
gies), ∂P1(∆T ,0,θ)∂θ
[∂d1∂∆1
]= −1/ (6θ). Together these two effects imply a positive impact of compe-
tition on the marginal benefit from innovation; and the business stealing effect, which simplifies to
∂d1(∆T ,0,θ)∂θ
[∂P1∂∆1
]= ∆T /18 > 0, accentuates this positive impact. Indeed, under targeted licensing,
competition raises the innovator’s marginal benefit from innovating, thereby increasing equilibrium
innovation ∆∗T .
Note that the differential strength of increased business stealing across licensing strategies comes
from the difference underlined at the beginning of Section 3. Under market-wide licensing, increased
business stealing exacerbates the decrease in Firm i laggard demand associated with an increase in
innovation ∆M . But in the laggard situation where Firm i does not purchase the license, it is left with
an innovation disadvantage relative to its rival, and relatively low margins in equilibrium, thus muting
the exacerbating effect of increased business stealing. In contrast, under targeted licensing, increased
business stealing amplifies the increase in Firm 1’s leader demand associated with an increase in ∆T .
This is a situation in which Firm 1 has an innovation advantage relative to its rival, and relatively
17
high margins in equilibrium, further magnifying the amplifying effect of increased business stealing.
3.3 Competition and Innovation in Equilibrium
Bringing together the results of Propositions 2 and 3, one can easily deduce the impact of competition
on equilibrium innovation:
Proposition 4 If the relative cost of market-wide licensing h is low to moderate - h ∈ (0, 1/6) - then
for all θ ∈ (0, θ∗ (h)) innovation ∆∗ = ∆∗M is strictly decreasing in competition, and for all θ ∈ [θ∗, 9/2)
innovation ∆∗ = ∆∗T is strictly increasing in competition. If h is high - h ≥ 1/6 - innovation ∆∗ = ∆∗T
is strictly increasing in competition for all θ ∈ Θ.
The intuition follows directly from the discussions of Propositions 2 and 3. We depict the results
of Proposition 4 in Figure 2 below:
[Insert Figure 2 here.]
Note that when the relative cost of market-wide licensing h is low to moderate - h ∈ (0, 1/6) -
equilibrium innovation may jump up or down depending on the value of h. To see this, first recall
from Proposition 3 that there exists a threshold level of competition θ∗∗ = 9/4 such that innovation
is greater under market-wide licensing for all θ ∈ (0, θ∗∗), and greater under targeted licensing for
all θ ∈ [θ∗∗, 9/2). Now if h is at the low end of (0, 1/6), then market-wide licensing is relatively
attractive, and the threshold level of competition θ∗ (h) at which the innovator switches from market-
wide licensing to targeted licensing is relatively high, higher in fact than θ∗∗ = 9/4. In this case
innovation jumps up at θ∗ (h). Conversely, if h is at the high end of (0, 1/6), then market-wide
licensing is relatively unattractive, and θ∗ (h) is relatively low and lower than θ∗∗ = 9/4. In that case
innovation jumps down at θ∗ (h).
At a broader level, the foregoing analysis suggests that the relationship between downstream inno-
vation and upstream innovation is inextricably linked to the innovator’s licensing strategy. Indeed, the
key empirical implication of Proposition 4 and Figure 2 is that as long as the transaction costs associ-
ated with market-wide licensing are not prohibitively high, we should observe a U-shaped relationship
between downstream competition and upstream innovation; with innovation decreasing in competition
at low levels of competition (when market-wide licensing is optimal), and increasing in competition at
high levels of competition (when targeted licensing is optimal). We test this empirical prediction in the
next two sections.
18
4 Testing the Model: Data and Variables
To test our model, we develop a data set from five sources. The sources bring together data on
innovation, competition, upstream-downstream relationships, and licensing deals.
4.1 IBISWorld Industry Linkages
First, to identify upstream and downstream industry relationship, we hand-collect data from 2008
IBISWorld reports. IBISWorld is an independent publisher of U.S. industry research, and its annual
reports use a variety of sources from government, company, to industry association statistics, provid-
ing information about market characteristics, supply-chain relationships, and so forth. We use the
information about supply-chain relationships to identify the downstream industries for each five-digit
NAICS industry. Specifically, we hand-collect the data on all five-digit NAICS industries and their
downstream industries; record the data into excel spreadsheet; we then have our data on upstream-
downstream relationships ready for analysis. Summary information is provided in Table 1, which
presents the average number of five-digit NAICS downstream industries for each two-digit NAICS
upstream industry group. Among these industry groups, manufacturing sectors have on average the
greatest number of downstream industries (134.5), while accommodation and food Services has on
average the fewest downstream industries (8).
[Insert Table 1 here.]
4.2 NBER Patent Citation Data
Next, we use the National Bureau of Economic Research (NBER) Patent Citation Database initially
created by Hall et al. (2001, 2005) to measure innovation activity. This database contains annual
information on patents and citations for publicly traded U.S. firms over the period 1976 − 2006. We
use information on citations to and from each patent to construct a count of citation-weighted patent
counts. Specifically, we first calculate the total number of patents firm i in industry j has in year t,
and then calculate the weight of firm i’s patents by using the patent citations that firm i has received
divided by the total patent citations that all sample firms have received in year t, and we then get
citation-weighted patent counts for firm i in industry j and year t,
CITATION−WEIGHTED PATENTSi,j,t = PATENT COUNTSi,j,t·∑
p PATENT CITATIONSi,j,p,t∑i
∑p PATENT CITATIONSi,j,p,t
,
19
where subscripts i, j, p, and t denote firm, industry, patent, and year, respectively; PATENT COUNTSi,j,t
captures the total patent count for firm i in industry j in year t; and PATENT CITATIONSi,j,p,t
represents the citations that patent p of firm i in industry j has received in year t.
We adjust our measure of innovation to address the truncation problem arising as the patents
appear in the database only after they are granted. We correct for the truncation related to the
citation counts as a patent can keep receiving citations over a long period of time, but we only
observe citations received up to 2006. Following Hall et al. (2001, 2005), we correct this truncation
bias by dividing the observed citation counts by the fraction of predicted lifetime citations actually
observed during the lag interval. More specifically, we scale up the citation counts using the variable
“hjtwt” provided by the NBER Patent Citation Database, which relies on the shape of the citation
lag distribution. The truncation-adjusted measures of patents and citation counts are used in all of
our tests.
We also use another two alternatives to proxy for upstream firm innovation: TOTAL PATENT
CITATIONSi,j,t, calculated as∑
p PATENT CITATIONSi,j,p,t; and TOTAL CITATIONS PER
PATENTi,j,t, computed as∑p PATENT CITATIONSi,j,p,tPATENT COUNTSi,j,t
.
4.3 Compustat Annual Industrial Data
Third, we collect financial data from Standard and Poor’s Compustat Annual Files to compute down-
stream industry competition. Specifically, we obtain data on firm sales, operating profits, gross profit
margin, financial costs, and industry code where proxies of industry competition based on the Lerner
index can be computed. We also collect a vector of control variables about firm and industry charac-
teristics from Compustat, which may affect firms’ innovation activity or licensing strategy.
We use the Compustat data to compute the Lerner index as a measure of the degree of industry
competition. In particular, the market measure of competition is defined as Cj,t = 1−∑nj,ti=1 Li,tnj,t
, where
j denotes the industry, i denotes a firm in the industry, and t is fiscal year. We follow Aghion et al.
(2005) and compute the Lerner index as Li,t = Operating profit −Financial costSales , where operating profits
net of depreciation provisions and an estimated financial cost of capital divided by sales measure the
price cost margin. In order to compute the competition level across all the firms in an industry, we
use the entire sample of Compustat in each industry, not only those in the patenting subsample.
We also use the Text-based Network Industry Classifications (TNIC) developed by Hoberg and
Philips (2010, 2016) to capture downstream industry competition in a way that is closer to the
20
“Hotelling”measure used in our model. Indeed, in our Hotelling model competition is captured by the
degree of homogeneity between products θ = 1/t, similar to the TNIC-based measure that is derived
from computing firms’ products similarities from the text analysis in their 10-K product descriptions.
The TNIC do seem to provide a good fit for our theoretical measure of competition, and hence we
perform our empirical analysis using TNIC-based industry competition as a robustness check.
We also use Compustat to compute a variety of firm and industry controls. All variables are
computed for firm i over its fiscal year t. In the baseline regressions, the control variables include
profitability, ROA, measured by return on assets; investment in innovation, R&D/ASSETS, measured
by R&D expenditures scaled by total assets; LEVERAGE, measured by total debt-to-total assets;
investment in fixed assets, CAPEX/ASSETS, measured by capital expenditures scaled by total assets;
growth opportunity; MARKET-TO-BOOK, measured by the firm’s market-to-book ratio. To control
for possible nonlinear effects of competition in the upstream market (Aghion et al., 2005), we also
include upstream product market competition (based on a Herfindahl index computed from annual
sales) and its squared term in our baseline regressions. Detailed variable definitions are described in
Table 2.
[Insert Table 2 here.]
4.4 SDC Strategic Alliance and Joint Venture Data
Fourth, we obtain data on firms’ licensing strategies from the Joint Venture & Strategic Alliance
database of Securities Data Company (SDC). We use SDC because it provides detailed information on
licensing deals across a variety of industry sectors, which is especially well-suited for our research on
downstream industry competition and upstream innovation.19 The SDC database records all publicly
announced alliance deals worldwide and provides detailed information about licensing deals, such as
licensing contract type (i.e. exclusive, non-exclusive, and cross licensing), the identities of licensors
and licensees, the SIC codes of the participants and alliances, and so forth. Note that by definition
exclusive and non-exclusive licensing strategies in the SDC database are analogous to the targeted
licensing and market-wide licensing in our theoretical model, respectively. Despite some limitations to
the SDC database, the information on licensing contract type, which is one of the main variables we
use in our model, is quite accurate (Anand and Khanna, 2000). Specifically, by reading through the
19SDC reports a comprehensive coverage on the formation of all kinds of alliances by companies and the licensing dealsamong them all over the world from 1988. Given this, the licensing activities in SDC would be a good representative ofour overall sample.
21
texts which describe the details about licensing deals, we hand-collect the data on whether a specific
participant is a licensor or a licensee, whether it is a licensing contract based on market-wide strategy
or targeted strategy, and whether the participants are licensing technology or not. We are also able
to eliminate the agreements for which the agreements are about termination of previous agreements
or litigation between participants, or less than two participants are involved.
4.5 Measuring Import Tariffs
Finally, we obtain import tariff data from Peter Schott’s International Economics Resource Page to
address the potential endogeneity of downstream industry competition (Schott, 2010). This Web Page
provides the data on imports by country and industry from 1989− 2005. We collect the import tariff
rates for all industries in the dataset and then calculate reductions in import tariff rates for each
industry in each year. We expect to use reductions in import tariff rates as an exogenous competitive
shock to address the potential endogeneity concerns for downstream competition.
4.6 Summary Statistics
We present a summary statistics of the U.S. data in Table 3. All data are annual. The time coverage
of the U.S. data is over the period 1976 − 2006 (31 years). At five-digit NAICS level, there are
319 industries with 24, 845 firm - year observations.20In order to mitigate the impact of outliers, we
winsorize all variables at the 1st and 99th percentiles.
[Insert Table 3 here.]
Table 3 presents means, medians, standard deviations, 10th and 90th percentiles for upstream firm
innovation, downstream industry competition, and control variables. The patenting activities in our
sample show typical skewness with a mean of 0.1362 citation-weighted patent counts and a median of
0.00239. Related measure citations per patent has a mean of 15.548 and a median of 10.485, which
suggests that each patent has on average 15.548 cites.
The summary statistics for downstream competition in Table 3 indicates that downstream industry
competition based on Lerner index has an average of 0.7687 and a median of 0.779. And the standard
deviation of downstream competition is 0.0699 across all the industries in U.S. from 1976 - 2006.
20The sample for our baseline model is U.S. public traded firms across all industries over the period 1976-2006. Wealso do our empirical analysis by excluding financial and utility firms, and using the sample only from manufacturingindustries as shown in Appendix A. We find that our main results are robust to samples with different industries.
22
Regarding other variables of interest, the average firm in our sample has a market-to-book ratio of
1.458, a R&D to assets ratio of 5.165%, a leverage ratio of 18.62%, capital expenditures over total
assets of 5.03%, and return on asset of 0.121. The upstream industry competition based on Herfindahl
has an average of 0.848 and a median of 0.601.
5 Main Findings
This section presents the main empirical findings in the paper. We begin by establishing a U-shaped
relationship between upstream innovation and downstream competition in line with the predictions
of the model. Then we discuss an instrumental variables strategy that allows us to assess the causal
impact of changes in competition on changes in innovation. The final piece of our empirical analysis
shows that licensing patterns vary with competition in a manner consistent with the model.
5.1 The Empirical Link between Competition and Innovation
We begin by estimating the following empirical relationship between downstream competition and
upstream innovation:
CITATION −WEIGHTED PATENTSi,j,t = β0 + β1 ·DOWNSTREAM COMPj,t +
β2 ·DOWNSTREAM COMP 2j,t + γ · Zi,t + δt + αj + εi,j,t, (17)
where CITATION −WEIGHTED PATENTSi,j,t denotes the citation-weighted patent counts for
firm i in industry j and year t, which captures upstream firm innovation level.21 Our main explanatory
variable of interest, downstream competition, represents the average product market competition of
all the downstream industries that relate to the upstream industry j in which firm i operates in year
t, i.e.
DOWNSTREAM COMPj,t =
∑k
DOWNSTREAM COMPj,k,t
nj,t,
where DOWNSTREAM COMPj,t is the average of the downstream industry competition level that
firms in upstream industy j face in year t; DOWNSTREAM COMPj,k,t is the competition level
in a downstream industry k related to the upstream industry j in year t; and nj,t is the number
of downstream industries related to the upstream industry j in year t. Finally, we include Zi,t, δt,
21As a robustness exercise, in Appendix A we also present results based on citations per patent and total citationsthat firm i in industry j has in year t as proxies for upstream firm innovation.
23
and αj as our control variables in the model specification. Among them, Zi,t is a vector of firm
level and industry level characteristics; δt represents year fixed effects and controls for changes in the
macroeconomic environment and systematic changes in patenting activities over time; and industry
fixed effects αj , based on five-digit NAICS industry dummies, control for any unobserved industry
heterogeneity that is time invariant and affects firm patenting activities.
[Insert Table 4 here.]
Our main dependent variables are discrete and non-negative, and to account for this, in our baseline
model we use a Negative Binomial model to investigate the impact of downstream industry competi-
tion on upstream firm innovation (Hashmi, 2013). We report our main empirical results in Table 4.
Specifically, in column (1) of Panel A, the coefficient estimates on DOWNSTREAM COMP and its
squared term, DOWNSTREAM COMP 2, are −8.541 and 6.659, and which are significant at the 5%
and 1% levels respectively. The effects are economically large. Because the derivative of innovation
with respect to downstream competition from Equation (17) is β1 + 2β2Cj,t, the negative sign for β1
and positive sign for β2 clearly support for a U-shaped relationship between downstream competition
and upstream innovation.
In column (2) of Panel A, we add firm R&D expenditure, leverage ratio, market-to-book value,
return on asset, capital expenditure as firm level controls into the Negative Binomial model specifica-
tion in column (1). Moreover, following Aghion et al. (2005), we include upstream competition and
its square to control for the impact of upstream industry competition on upstream firm innovation.
We control for year and industry fixed effects as well. The results in column (2) show that the coeffi-
cient estimates on DOWNSTREAM COMP and DOWNSTREAM COMP 2 remain significantly
negative and positive respectively. This again provides support for the U-shaped relationship between
downstream competition and upstream innovation.
In columns (3) − (7), we consider two alternative models, OLS and Poisson model, respectively.
In particular, in columns (3)− (5) of Panel A we estimate the impact of downstream competition on
upstream innovation by using OLS method, where the dependent variable becomes the logarithm of one
plus citation-weighted patent counts of firms. Specifically, column (3) shows the results of the impact
of downstream competition on upstream innovation. The coefficients of DOWNSTREAM COMP
and DOWNSTREAM COMP 2 are −3.334 and 1.983 respectively, and both are significant at the
5% level. Columns (4) and (5) add firm and industry characteristics, year fixed effects, and industry
24
fixed effects. The coefficients of DOWNSTREAM COMP and DOWNSTREAM COMP 2 remain
significantly negative and positive respectively.
In columns (6) and(7), we present the results of the effect of downstream competition on up-
stream innovation in a Poisson regression. As shown in column (6), the coefficient estimates on
DOWNSTREAM COMP and DOWNSTREAM COMP 2 are −3.241 and 2.680, and both are
significant at the 10% and 5% levels, respectively. Firm and industry level controls are added
into the model specification in column (7). The coefficients of DOWNSTREAM COMP and
DOWNSTREAM COMP 2 remain significantly negative and positive respectively. These results
provide consistent support for the U-shaped relationship between downstream competition and up-
stream innovation when estimating based on the Poisson model, and controlling for firm and industry
characteristics, year and industry fixed effects.
As a robustness check, we use the Text-based Network Industry Classifications (TNIC) of Hoberg
and Philips (2016) as an alternative industry classification system. The TNIC are obtained by com-
puting firm pairwise similarity scores from text analysis in firms’ 10-K product descriptions. The
similarities-based TNIC provide a good fit to our theoretical model, where competition is captured by
the degree of homogeneity between products. Specifically, Hoberg and Philips (2010, 2016) develop
the FIC industry classification which is based on an algorithm clustering firms together to maximize
within-industry similarity. In their dataset, they include FIC-500, FIC-400, FIC-300, FIC-200, FIC-
100, FIC-50 and FIC-25 industries to represent 500, 400, 300, 200, 100, 50, 25 different industry groups
respectively. Following Hoberg, Phillips, and Prabhala (2014), we use FIC-300 industries to compute
the TNIC-based HHI index for each downstream industry.22 Consistent with our baseline model in
Table 4, we adopt a Negative Binomial model for the analysis, and control for R&D expenditure,
leverage ratio, market-to-book value, return on asset, capital expenditure, upstream industry compe-
tition and its square term, which may affect firms’ innovative activities. We also include year fixed
effects and industry fixed effects into the specification. All standard errors are adjusted for within-firm
clustering.
[Insert Table 5 here.]
The results are presented in Table 5. As shown in column (1), the coefficient estimates on
DOWNSTREAM COMP (TNIC), a TNIC-based downstream industry competition measure, and
22We also try FIC-500, FIC-400, FIC-200, FIC-100 and find that our results are robust to these different industrygroups.
25
its square term, DOWNSTREAM COMP (TNIC)2, are -4.027 and 6.023 respectively, and both
are significant at the 5% level. In column (2), we include the following control variables into the
model specification: R&D expenditure, leverage ratio, market-to-book value, return on asset, capital
expenditure, upstream industry competition and its square term. We obtain significant results similar
to those presented in column (1). We further control for year fixed effects and industry fixed effects
in column (3). The coefficient estimates on both TNIC-based downstream competition and its square
term remain significant at the 1% or 5% level, depending on the specification and variable. In all, the
results presented in Table 5 suggest that the U-shaped relationship between downstream competition
and upstream innovation still holds when using the TNIC-based industry competition measure.
We also consider a number of additional robustness checks. In particular, to address the concern
that a significant coefficient on the square term of downstream competition is necessary but insufficient
to establish a quadratic U-shaped relationship, we 1) verify that the threshold level of competition at
which innovation is minimized is indeed within the range of values for downstream industry competi-
tion; and 2) split our data sample into different percentiles to verify that the impact of downstream
competition on upstream innovation is negative at low levels of competition and positive at high levels
of competition. These and other robustness checks yield results that are consistent with our baseline
results, and are discussed in more detail in Appendix A.
5.2 Does Competition Cause Innovation?
One potential concern in the analysis presented above relates to the endogeneity of downstream in-
dustry competition. In general, some omitted factor like expected industry profitability or market size
might jointly affect downstream industry structure and upstream firm innovation.
To address the potential endogeneity of downstream industry competition, we use an instrumen-
tal variable strategy designed to isolate exogenous changes to downstream industry competition by
exploiting changes in tariffs. With the globalization of the economic activities and trade openness,
domestic firms are increasingly exposed to the competition from foreign rivals (Bernard, Jensen, and
Schott, 2006). Reductions in import tariff rates significantly decrease the cost for foreign firms to enter
U.S. product markets and therefore increase the presence of goods and services from foreign rivals.
This penetrations of imports spurs an increase in the competitive pressure that domestic firms face in
product markets.
We follow Fresard (2010) and Valta (2012) and use large reductions of import tariff rates as events
26
that trigger a sudden increase in the competitive pressure faced by domestic firms. We gather U.S.
import data compiled by Schott (2010) for the sample period 1989 – 2005. For each industry–year,
we compute the ad valorem tariff rate as the duties collected at U.S. Customs divided by the Free-
On-Board custom value of imports. We then characterize “competitive shocks” as large variations in
the tariff rate in terms of the deviation of the yearly change in tariff rates from the same industry’s
median or average change. To do so, we first compute for each industry the median (or average) tariff
rate change as well as the largest tariff rates changes. Then we define a competitive shock for each
downstream industry as a dummy variable, IMPORT TARIFF CHANGEk,t, which equals one if
the largest tariff rate reduction in downstream industry k by year t is larger than three times the
median tariff rate reduction in that industry; and zero otherwise.23 Finally, based on the upstream-
downstream industry relationships we identified, we take the average of competitive shocks coming
from the downstream industries associated with a specific upstream industry j. We then get the
average of downstream industry competition for the upstream industry j in year t, i.e., IMPORT
TARIFF CHANGEj,t =∑k IMPORT TARIFF CHANGEk,t
nj,t, where nj,t is the number of downstream
industries related to the upstream industry j in year t.
[Insert Table 6 here.]
Table 6 presents the estimation results. Column (1) presents the result of the first stage. In partic-
ular, we regress downstream competition on the competitive shock, controlling for R&D expenditure,
firm leverage, market-to-book ratio, ROA, capital expenditure, and upstream industry competition
and its square term. We also control for year fixed effects and industry fixed effects in the estimation.
As shown in column (1), the coefficient of IMPORT TARIFF CHANGE has a value of 0.02, and
is positive and significant at the 1% level. And the F-value is 431.7, well above the conventional level
of 10 advocated by Stock and Yogo (2005). These suggest that reductions in import tariff rate as the
instrument is correlated with the endogenous explanatory variable, downstream competition, and we
have a strong first stage.
Because we only have a single instrument but we wish to capture a quadratic relationship in
the data, we split our sample into two subsamples by using the threshold point of the U-shaped
relationship. This threshold point determined analytically by applying the regression estimates from
23We also try two alternatives in Appendix A, defining the competitive shock by whether the largest tariff rate reductionis larger than two times (or one and a half) the median tariff rate reduction. Our results are robust to different definitionsof competitive shock.
27
Table 4 into the formula for the derivative of innovation with respect to downstream competition,
setting this derivative to zero and solving for the threshold degree of competition. Having determined
the threshold, we then use the predicted value from the first stage regression as the instrumented
regressor in each sub-sample regression. Columns (2) - (4) report the result of the second stage using
the subsample below the threshold point of downstream competition. Specifically, in column (2), we
regress upstream innovation on the predicted value of downstream competition from the first stage,
controlling for R&D expenditure, firm leverage, market-to-book ratio, ROA, capital expenditure, and
upstream industry competition and its square term. Column (2) shows that the coefficient estimate
on DOWNSTREAM COMP (Fitted) is negative and significant at the 1% level, suggesting that
downstream competition has a negative relationship with upstream innovation. In columns (3) and
(4), we further control for year fixed effects and industry fixed effects, respectively. The coefficient
of DOWNSTREAM COMP (Fitted) remains negative and significant - at the 5% and 10% levels,
respectively - in these two columns. These provide empirical support for the left hand side of the
U-shaped relationship. In other words, when downstream competition is below a threshold point,
upstream innovation is decreasing in downstream industry competition.
Columns (5) - (7) show the results of the second stage using the subsample above the threshold
point of downstream competition. Column (5) shows that the effect of downstream competition on
upstream innovation is positive and significant at the 1% level, after controlling for R&D expenditure,
firm leverage, market-to-book ratio, ROA, capital expenditure, and upstream industry competition
and its square term. We add year fixed effects and industry fixed effects in columns (6) and (7),
respectively, and find that the impact of downstream competition on upstream innovation remains
significantly positive - at the 5% and 10% levels, respectively - in these two columns. These indicate
that upstream innovation is increasing in downstream competition when downstream competition is
above a threshold point. i.e., the right hand side of the U-shaped relationship is supported by our
empirical evidence as well.
[Insert Table 7 here.]
As an additional robustness check, we split the sample at the median level of industry concentration
and repeat our split-sample IV strategy. These results are presented in Table 7, and are qualitatively
similar to those presented in Table 6.
28
5.3 Exploring the Licensing Channel
While the above results show that downstream industry competition has a U-shaped impact on up-
stream firm innovation, they are silent on whether licensing considerations are central to this relation-
ship. In this section, we investigate the role that upstream firms’ licensing strategies play.
Two licensing-related empirical implications emerge from our theoretical model. First, downstream
competition has a negative impact on upstream innovation under market-wide licensing and a positive
impact on upstream innovation under targeted licensing. And second, competition increases the appeal
of targeted licensing relative to market-wide licensing.
To investigate these conjectures, we use the licensing deal data from the Strategic Alliance database
of Securities Data Company (SDC), which we described above in Section 4. Because SDC focuses more
on U.S. firms, and because the deal sample prior to 1990 is incomplete, we restrict our analysis to the
licensing deals between public U.S. firms from 1990− 2006. We start an initial set of 5, 908 licensing
deals announced from January 1, 1990 to December 31, 2006, corresponding to 6,870 companies
traded in the United States. Merging Compustat and SDC data give us a sample with 1,415 firm-year
observations. Our final step of data collection is to link the merged dataset with the NBER Patent
Citation Dataset, obtaining firms’ information on patenting since January 1, 1990. This gives us a
final sample of 605 observations, with 631 licensors and licensees traded in United States. Typically,
within an industry, the number of licensors varies from 1 to 50, with a median of 4. Therefore, we add
upstream industry concentration in our regressions to control for the impact of upstream competitors
on the upstream firm’s innovation.
To examine the first conjecture, we consider the impact of downstream competition and licensing
strategy on upstream innovation. Panel A of Table 8 presents the results. Specifically, for the same
reasons as in the baseline model, we again employ a Negative Binomial model here. The dependent vari-
able is CITATION−WEIGHTED PATENTS. The independent variables are DOWNSTREAM
COMP , representing downstream industry competition level; LICENSE TARGETED, a dummy
setting to 1 if targeted licensing is used, and zero otherwise; and an interaction of DOWNSTREAM
COMP and LICENSE TARGETED. We also include a vector of firm level and industry level char-
acteristics that may impact a firm’s future innovation productivity, i.e., R&D expenditure, leverage
ratio, market-to-book value, return on asset, capital expenditure, upstream industry competition and
its square term. As well, we include year fixed effects, to control for the impact of some variables
that change over time, and industry fixed effects, to control for time-invariant industry differences.
29
The results presented in Panel A of Table 8 are consistent with the predictions of our model. In
particular, as shown in column (1), the coefficient estimate on DOWNSTREAM COMP is nega-
tive with a value of 8.654, and significant at the 1% level, suggesting that downstream competition
has a negative impact on upstream innovation under market-wide licensing. Moreover, the coefficient
estimate on the interaction term is positive with a value of 12.097, and significant at the 1% level.
Thus, under targeted licensing downstream competition has a positive impact on upstream innovation
(12.097 − 8.654 = 3.443 > 0). We add a vector of firm level and industry level characteristics in the
model specification in column (2), and get similar results to those presented in column (1). In col-
umn (3), we further control for year fixed effects and industry fixed effects. The coefficient estimates
on DOWNSTREAM COMP and the interaction term remain significantly negative and positive,
respectively. In sum, the results presented in Panel A of Table 8 provide support for the first con-
jecture, namely that downstream competition has a negative impact on upstream innovation under
market-wide licensing and a positive impact on upstream innovation under targeted licensing.
[Insert Table 8 here.]
To examine the second conjecture, we empirically consider how downstream industry competition
impacts the appeal of targeted licensing relative to market-wide licensing. Panel B of Table 8 presents
the results regarding the impact of downstream competition on upstream firms’ licensing choices. In
particular, we look at how the propensity to apply a targeted licensing strategy is determined by the
product market competition level in the downstream industries. The dependent variable is LICENSE
TARGETED, and the independent variable is DOWNSTREAM COMP . We also include a vector
of firm level and industry level characteristics, which may affect the choice of licensing strategies, into
our model specification (Anand and Khanna, 2000; Kim and Vonortas, 2006; and Somaya, Kim, and
Vonortas, 2010). Specifically, we control for firm level characteristics such as firm size, prior license (a
proxy for whether a focal firm issued licenses before or not), knowledge stock, and complexity (a proxy
for the complexity of technology); and for industry level characteristics such as industry concentration,
industry growth, and IPR strength. We also control for year fixed effects and industry fixed effects.
All standard errors are adjusted for within-firm clustering. As shown in column (1), the coefficient
estimate on DOWNSTREAM COMP is positive and significant at the 1% level, suggesting that
downstream industry competition increases the appeal of targeted licensing relative to market-wide
licensing. In columns (2) and (3), we include firm and industry level characteristics, and year and
30
industry fixed effects, respectively. All of the coefficient estimates on DOWNSTREAM COMP
remain positive and significant. In all, consistent with the second conjecture, the results presented in
Panel B of Table 8 suggest that competition increases the appeal of targeted licensing over market-wide
licensing.
6 Conclusion
This paper develops a model in which technology markets mediate the effects of downstream competi-
tion and upstream innovation. When an upstream innovator can choose between a targeted licensing
strategy to one downstream competitor or a market-wide licensing strategy to both competitors si-
multaneously, we characterize an equilibrium threshold level of competition below which market-wide
licensing is optimal and innovation is decreasing in competition, and above which targeted licensing is
optimal and innovation is increasing in competition. When we take the model to the data we find clear
evidence of a U-shaped relation between downstream competition and upstream innovation. Licensing
patterns are a key mechanism behind this relation.
Our analysis suggests several directions for future research. In order to provide clear, stark and
tractable results, we make strong assumptions and develop a stylized model. In this context, it is
natural to question the optimality of the licensing contract. While much of the licensing literature
discussed in the introduction debates the circumstances under which fixed fees, auctions, royalties, or
two-part tariffs might be optimal, in this paper we abstract from this debate and motivate assumptions
about contractual incompleteness and transaction costs in order to ensure the (de facto) optimality
of the simplest of licensing contracts: the fixed fee. In Appendix C, we discuss what would happen in
auction and two-part tariff contexts, and show that the results are very similar to those of the main
model.
Another natural question concerns the robustness of our results to demand specifications other than
Hotelling. Competition affects our models in two ways - by affecting equilibrium levels of innovation,
and through the licensing payoffs received by the innovator. Targeted licensing allows one firm to
gain a cost advantage over its rival, yielding strong demand and large markups, which in turn amplify
the positive effects of competition. In contrast, market-wide licensing allows firms to not fall behind
their competitor; if they did they would have low demands and thin markups. In this market-wide
context, the positive effects of competition are muted by these low demands and markups. Although a
31
Hotelling demand framework provides simplicity, we believe that the intuition behind our main results
are quite general. Our conjecture is that qualitatively similar results would obtain in other address
models (e.g. Salop, 1979), as well as in logit models and in CES models a la Dixit-Stiglitz (1977).
Modeling the impact of competition under the demand specifications just enumerated is a natural and
appealing extension of this model, and one which we look forward to examining in future research.
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35
Tab
le1:
Sam
ple
Dis
trib
uti
onA
cros
sIn
du
stry
Th
ista
ble
rep
ort
sth
enu
mb
erof
firm
-yea
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serv
ati
ons
wit
hin
each
two-d
igit
NA
ICS
ind
ust
rygro
up
inou
rfi
nal
sam
ple
.T
his
tab
leals
ore
port
sfo
rea
chtw
o-d
igit
NA
ICS
ind
ust
rygro
up
the
mea
nvalu
esof
the
nu
mb
erof
cust
om
erin
du
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efin
edat
the
five-
dig
itN
AIC
Sle
vel
).
NA
ICS
cod
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stry
grou
pn
ame
Fir
m-y
ears
%of
Sam
ple
#D
ownst
ream
Ind
.
11A
gric
ult
ure
,F
ores
try,
Fis
hin
gan
dH
unti
ng
570.2
380
21M
inin
g57
72.3
142
22U
tili
ties
189
0.7
616
23C
onst
ruct
ion
660.2
663
31M
anu
fact
uri
ng
I77
73.1
178
32M
anu
fact
uri
ng
II59
2523.7
1191
33M
anu
fact
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ng
III
1367
754.7
4226
42W
hol
esal
eT
rad
e20
30.8
1231
44R
etai
lT
rad
eI
370.1
541
45R
etai
lT
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eII
150.0
647
48T
ran
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onan
dW
areh
ousi
ng
I15
00.6
068
49T
ran
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ng
II5
0.0
225
51In
form
atio
n13
575.4
354
52F
inan
cean
dIn
sura
nce
488
1.9
545
53R
eal
Est
ate
and
Ren
tal
and
Lea
sin
g25
81.0
348
54P
rofe
ssio
nal
,S
cien
tific
and
Tec
hn
ical
Ser
vic
es81
93.2
892
56A
dm
inis
trat
ion
,B
usi
nes
sS
up
por
t&
Was
teM
anag
emen
tSer
vic
es16
20.6
569
61E
du
cati
onal
Ser
vic
es22
0.0
921
62H
ealt
hca
rean
dS
oci
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ssis
tan
ce14
30.5
737
71A
rts,
Ente
rtai
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and
Rec
reat
ion
40.0
222
72A
ccom
mod
atio
nan
dF
ood
Ser
vic
es56
0.2
28
Tot
al24
,987
100.0
0
36
Table 2: Variable Definitions
This table reports summary statistics for variables constructed using a sample of U.S. public firmsfrom 1976-2006. All variables are measured annually at the firm level or industry level.
CITATION-WEIGHTED PATENTS The number of patents a firm receives in a given year weighted bythe citations of these patents.
TOTAL PATENT CITATIONS The total citations in a given year to patents that a firm has.TOTAL CITATIONS PER PATENT The total citations in a given year, divided by that year’s total
number of patents.DOWNSTREAM COMP One minus the Lerner index for a downstream industry.DOWNSTREAM COMP (TNIC) One minus the HHI index for a downstream industry based on
FIC-300 TNICR&D / ASSETS The ratio of Compustat research and development expenditures to
the book value of total assets, measured at the end of the fiscalyear.
LEVERAGE Book value of debt divided by book value of total assets measuredat the end of fiscal year
MARKET-TO-BOOK Market value of equity plus book value of assets minus book valueof equity minus balance sheet deferred taxes divided by book valueof assets.
ROA Operating income before depreciation divided by book value oftotal assets, measured at the end of fiscal year
CAPEX/ASSETS Capital expenditures scaled by book value of total assets measuredat the end of fiscal year t.
UPSTREAM COMP One minus the Herfindahl index of four-digit SIC industry j towhich firm i belongs, measured at the end of fiscal year t.
LICENSE TARGETED A dummy variable setting to 1 if targeted licensing strategy isadopted, and 0 if market-wide licensing is used.
FIRM SIZE Log of firm sales amount in a given year.PRIOR LICENSE A dummy variable setting to 1 if a licensor firm had sold licenses
up to period t-1, and 0 otherwise.KNOWLEDGE STOCK The number of patents granted to the firm in year t, plus the
number of patents granted to the firm up to year t-1, depreciatedby 15%.
COMPLEXITY A dummy variabel setting to 1 if the two-digit SIC industry thata firm operates in is equal to or above 35, and 0 otherwise.
INDUSTRY CONCENTRATION One minus the Lerner index based on four-digit SIC industries.INDUSTRY GROWTH The percentage change in total sales in four-digit SIC industries.IPR STRENGTH Proxied by industry patent intensity, measured by industry patents
divided by industry R&D expenditure in a given year.
37
Table 3: Summary StatisticsThis table reports summary statistics for variables constructed using a sample of U.S. public firmsfrom 1976-2006. All variables are measured annually at the firm level or industry level. Variabledefinitions are provided in Table 2.
VARIABLES 10% Pctile. Mean Median 90% Pctile. Std. Dev. Obs.
CITATION-WEIGHTED PATENTS 0.000 0.1362 0.002 0.059 0.777 24,845TOTAL PATENT CITATIONS 1.046 423.6158 37.990 629.598 2335.598 24,915TOTAL CITATIONS PER PATENT 0.620 15.548 10.485 33.178 20.456 24,915DOWNSTREAM COMP 0.682 0.7687 0.779 0.844 0.071 24,915R&D/ASSETS 0.009 0.1081 0.052 0.251 0.168 20,780LEVERAGE 0.000 0.2154 0.186 0.450 0.202 24,785MARKET-TO-BOOK 0.888 2.257 1.458 4.242 2.372 21,498ROA -0.238 0.0442 0.121 0.240 0.292 24,697CAPEX/ASSETS 0.016 0.0632 0.050 0.124 0.051 24,378UPSTREAM COMP 0.601 0.848 0.926 0.987 0.190 24,914
38
Table 4: Downstream Competition and Upstream Innovation
This table presents coefficients estimates of regressions which examine the effect of downstream industry competition on upstreamfirm innovation (equ. (17)). The dependent variable is CITATION-WEIGHTED PATENTS for firm i in industry j and year t.Column (1) presents the results with year and industry fixed effects by using negative binomial method, and column (2) furtherincludes firm level and industry level controls. Column (3) presents the results by using OLS, and columns (4) and (5) based onOLS include year and industry fixed effects, and control for firm characteristics respectively. Finally, columns (6) and (7) showthe results by using poisson model with year and industry fixed effects and firm and industry level controls. The sample period isfrom 1976-2006. All variables are defined in Table 2. The t-statistics reported in parentheses below the coefficient estimates arebased on standard errors adjusted for within-firm clustering. Significance at the 10%, 5%, and 1% level is indicated by *, **, ***,respectively.
VARIABLES (1) (2) (3) (4) (5) (6) (7)
DOWNSTREAM COMP -8.541** -7.001* -3.334** -3.796** -1.500* -3.241* -5.287*(3.674) (3.953) (1.326) (1.510) (0.908) (1.806) (2.861)
DOWNSTREAM COMP2 6.659*** 5.677** 1.983** 2.237** 1.004* 2.680** 4.22**(2.532) (2.760) (0.830) (0.930) (0.556) (1.390) (2.160)
R & D / ASSETS -11.137*** -0.086* -0.139* -10.445***(2.746) (0.050) (0.070) (3.513)
LEVERAGE 0.203 0.010 0.063* 0.257(0.538) (0.026) (0.032) (0.481)
MARKET-TO-BOOK -0.240*** -0.004*** -0.004*** -0.207***(0.077) (0.001) (0.001) (0.065)
ROA 3.404*** 0.024 0.030 2.073***(0.613) (0.025) (0.025) (0.753)
CAPEX/ASSETS 3.995** 0.155 0.096 1.785(1.982) (0.147) (0.155) (1.800)
UPSTREAM COMP -3.358* 0.326* -0.134 -2.565(1.972) (0.188) (0.100) (2.202)
UPSTREAM COMP2 2.316 -0.247 (0.069) 1.515(1.578) (0.165) (0.103) (1.815)
Fixed Effects:Year Yes Yes No No Yes Yes YesIndustry Yes Yes No No Yes Yes Yes
Method NB NB OLS OLS OLS Poisson PoissonClusters 3,718 2,716 3,718 2,716 2,716 3,718 2,716Observations 24,845 17,743 24,845 17,743 17,743 24,845 17,743
39
Table 5: Innovation and Downstream Competition with Alternative IndustryThe dependent variable in each specification is CITATION-WEIGHTED PATENTS for firm i in industry j andyear t. Industry classifications are based on Hoberg and Phillips (2010, 2016) text-based industry classifications,which form industries based on text analysis of 10-K reports. All variables are defined in Table 2. The t-statisticsreported in parentheses below the coefficient estimates are based on standard errors adjusted for within-firmclustering. Significance at the 10%, 5%, and 1% level is indicated by *, **, ***, respectively.
VARIABLES (1) (2) (3)
DOWNSTREAM COMP (TNIC) -4.027** -5.166*** -5.444***(1.590) (1.974) (2.005)
DOWNSTREAM COMP(TNIC)2 6.023** 7.331** 7.640***(2.524) (3.161) (3.211)
R&D/ASSETS -4.549*** -4.436***(1.299) (1.257)
LEVERAGE 0.679** 0.708**(0.333) (0.326)
MARKET-TO-BOOK -0.0846** -0.0827**(0.039) (0.038)
ROA 3.601*** 3.592***(0.475) (0.480)
CAPEX/ASSETS 1.187 1.149(1.395) (1.411)
UPSTREAM COMP -2.179(1.561)
UPSTREAM COMP2 1.350(1.471)
Year fixed effects Yes Yes YesIndustry fixed effects Yes Yes YesClusters 2349 1800 1800Observations 9448 7140 7140
40
Table 6: Split-sample IV Regressions: Imputed SplitsThis table reports instrumental variables regressions of upstream innovation on downstream compe-tition. The first stage, reported in column (1), is an OLS regression of downstream competition onthe RHS variables reported in the table. In this specification, the instrument is the change in tariffrates in the industry, based on data obtained from Schott (2010). We first compute for each indus-try the median tariff rate change as well as the largest tariff rates changes. Then we define for eachdownstream industry the dummy variable, IMPORT TARIFF CHANGEk,t, which equals one if thelargest tariff rate reduction in downstream industry k by time t is larger than three times the mediantariff rate reduction in that industry; and zero otherwise. Then we average the competitive shockscoming from the downstream industries associated with an upstream industry. Then we split thesample according to whether the industry in question is above or below the peak implied by the linearand quadratic terms in Column (5) of Table 4. In columns (2)-(4), we regress upstream innovation ondownstream competition for below-peak levels of industry competition, using the generated regressorfrom the first stage as an instrument for downstream competition. Columns (5)-(7) repeat the sameanalysis but focus on the set of industries with above-peak competition each year. The sample periodis from 1976-2006. All variables are defined in Table 2. The t-statistics reported in parentheses belowthe coefficient estimates are based on standard errors adjusted for within-firm clustering. Significanceat the 10%, 5%, and 1% level is indicated by *, **, ***, respectively.
First Stage 2nd Stage-Below Cut 2nd Stage-Above CutVARIABLES (1) (2) (3) (4) (5) (6) (7)
DOWNSTREAM COMP(Fitted) -24.91*** -30.73** -64.75* 9.97*** 18.36** 21.08*(9.379) (12.492) (36.160) (3.218) (7.694) (11.440)
IMPORT TARIFF CHANGE 0.02***(0.002)
R&D/ASSETS -0.01 5.51 6.71 13.21*** -9.87** -10.79*** -16.54***(0.010) (4.384) (4.507) (4.219) (4.253) (4.106) (4.579)
LEVERAGE -0.00 -2.67* -3.11** -5.73*** -1.39 -1.41 0.13(0.004) (1.388) (1.450) (1.611) (1.201) (1.183) (1.212)
MARKET-TO-BOOK 0.00** 0.07 0.12 0.17 -0.39*** -0.40*** -0.43***(0.001) (0.297) (0.245) (0.280) (0.110) (0.111) (0.139)
ROA 0.00 9.94*** 9.56*** 12.74*** 1.06 1.21 2.60**(0.004) (1.874) (1.943) (1.943) (1.325) (1.456) (1.220)
CAPX/ASSETS 0.00 17.31*** 17.87*** 3.00 10.22*** 11.25*** 12.24***(0.016) (5.189) (5.865) (8.546) (3.883) (4.072) (3.823)
UPSTREAM COMP -0.04 5.21 5.06 -1.56 3.55 5.88 1.14(0.032) (5.452) (5.118) (7.867) (3.514) (3.947) (4.149)
UPSTREAM COMP2 0.06** -6.32 -5.90 -4.30 -2.51 -4.89 -3.04(0.025) (5.349) (4.812) (7.340) (2.676) (3.059) (3.538)
Year Fixed Effects Yes No Yes Yes No Yes YesIndustry Fixed Effects Yes No No Yes No No YesObs. 3,620 530 530 530 3,090 3,090 3,090R2 0.537 0.282 0.316 0.459 0.0538 0.0622 0.205F-test 431.7
41
Table 7: Split-sample IV Regressions: Median SplitsThis table reports instrumental variables regressions of upstream innovation on downstream compe-tition. The first stage, reported in column (1), is an OLS regression of downstream competition onthe RHS variables reported in the table. In this specification, the instrument is the change in tariffrates in the industry, based on data obtained from Schott (2010). We first compute for each industrythe median tariff rate change as well as the largest tariff rates changes. Then we define for eachdownstream industry the dummy variable, IMPORT TARIFF CHANGEk,t, which equals one ifthe largest tariff rate reduction in downstream industry k by time t is larger than three times themedian tariff rate reduction in that industry; and zero otherwise. Then we average the competitiveshocks coming from the downstream industries associated with an upstream industry. Then we splitthe sample according to whether the industry in question is above or below the median industry con-centration each year. In columns (2)-(4), we regress upstream innovation on downstream competitionfor below-median levels of industry competition, using the generated regressor from the first stage asan instrument for downstream competition. Columns (5)-(7) repeat the same analysis but focus onthe set of industries with above-median competition each year. The sample period is from 1976-2006.All variables are defined in Table 2. The t-statistics reported in parentheses below the coefficientestimates are based on standard errors adjusted for within-firm clustering. Significance at the 10%,5%, and 1% level is indicated by *, **, ***, respectively.
First Stage 2nd Stage-Below Cut 2nd Stage-Above CutVARIABLES (1) (2) (3) (4) (5) (6) (7)
DOWNSTREAM COMP (Fitted) -0.61 -23.11*** -39.49*** 18.39*** 13.64*** 23.56*(6.294) (6.328) (9.694) (3.862) (2.915) (13.624)
IMPORT TARIFF CHANGE 0.02***(0.002)
R&D/ASSETS -0.01 -5.74 -15.93*** -17.87*** -8.13** -12.77*** -13.35***(0.010) (4.060) (4.660) (4.740) (4.033) (4.549) (4.530)
LEVERAGE -0.00 -1.44 0.02 -0.09 -2.55* -1.04 -1.20(0.004) (1.847) (1.460) (1.429) (1.526) (1.489) (1.454)
MARKET-TO-BOOK 0.00** -0.33** -0.29* -0.33** -0.46*** -0.47*** -0.48***(0.001) (0.139) (0.152) (0.165) (0.120) (0.135) (0.152)
ROA 0.00 1.55 2.92* 4.14*** 2.38** 2.48** 3.64***(0.004) (1.479) (1.639) (1.581) (1.200) (1.155) (1.241)
CAPEX/ASSETS 0.00 2.46 4.30 7.47* 13.75*** 13.41*** 14.24***(0.016) (4.688) (3.763) (4.052) (4.150) (3.945) (4.258)
UPSTREAM COMP -0.04 2.46 -0.48 -3.11 26.58 2.61 3.03(0.032) (3.358) (4.454) (5.289) (19.772) (4.664) (4.801)
UPSTREAM COMP2 0.06** -2.15 -1.11 1.63 -17.44 -2.45 -3.54(0.025) (2.879) (3.549) (4.463) (12.856) (3.657) (3.855)0.80*** -0.71 10.29** 21.62*** -25.16*** -28.82 -38.56(0.012) (5.018) (5.222) (7.117) (8.311) (.) (.)
Year Fixed Effects Yes No Yes Yes No Yes YesIndustry Fixed Effects Yes No No Yes No No YesObservations 3,620 1,733 1,733 1,733 1,887 1,887 1,887R2 0.537 0.0243 0.244 0.259 0.0872 0.188 0.198F-test 431.7
42
Table 8: Downstream Competition, Licensing, and InnovationThis table captures the interaction between downstream competition, licensing, and innovation. In Panel A,the dependent variable is CITATION-WEIGHTED PATENTS for firm i in industry j and year t. And thedependent variable in Panel B is LICENSE TARGETED. All variables are defined in Table 2. The t-statisticsreported in parentheses below the coefficient estimates are based on standard errors adjusted for within-firmclustering. Significance at the 10%, 5%, and 1% level is indicated by *, **, ***, respectively.
Panel A
VARIABLES (1) (2) (3)
DOWNSTREAM COMP -8.654*** -6.345** -2.083*(2.354) (1.443) (1.240)
LICENSE TARGETED -13.372*** -11.439*** -5.001**(3.812) (3.607) (2.453)
DOWNSTREAM COMP* 12.097** 10.208*** 4.944*LICENSE TARGETED (3.923) (3.780) (2.652)LEVERAGE 5.155* 2.824*
(2.977) (1.573)MARKET-TO-BOOK -1.091*** -0.612***
(0.158) (0.171)ROA 9.587*** 8.115***
(1.360) (1.495)CAPEX/ASSETS -6.875 -5.034
(4.582) (3.681)UPSTREAM COMP 13.273 -23.081*
(10.052) (12.827)UPSTREAM COMP2 -8.595 13.423
(7.500) (9.033)Year fixed effects No No YesIndustry fixed effects No No YesObservations 567 472 472
Panel B
VARIABLES (1) (2) (3)
DOWNSTREAM COMP 0.523*** 0.348** 0.253*(0.114) (0138) (0.145)
FIRM SIZE 0.002 0.007(0.007) (0.010)
PRIOR LICENSE -0.053* -0.022(0.030) (0.040)
KNOWLEGE STOCK -0.001* -0.001*(0.000) (0.000)
COMPLEXITY -0.162** 0.089(0.042) (0.121)
INDUSTRY CONCENTRATION -0.029** -0.015(0.012) (0.018)
INDUSTRY GROWTH 0.039 -0.022(0.093) (0.095)
IPR STRENGTH 0.072 0.093(0.047) (0.125)
Year fixed effects No No YesIndustry fixed effects No No YesObservations 583 567 567
43
A Appendix: Empirical Robustness
This appendix discusses four robustness checks performed on the main empirical tests in the paper.
The regression results and associated tables discussed below are suppressed for brevity, but are available
from the authors upon request.
First, to address the concern that a significant coefficient on the square term of downstream
competition is necessary but not sufficient to establish a quadratic U-shaped relationship (Hanns et
al., 2016), we perform the following checks: (1) We check whether the threshold point is within our data
range. As we have checked, the range of our independent variable, downstream industry competition, is
from 0.42 to 0.88, and all the threshold points are within our data range. Taking column (2) in Table 4
in our baseline model as an example, the turning point of the U-shaped relationship is 0.6165(7.001/(2∗5.677) = 0.6165), which is clearly within our data range. (2) We split our data sample into different
percentiles to see how the relationship between downstream competition and upstream innovation
varies with the subsamples. We first run simple regressions of upstream innovation on downstream
competition using the 10th, 15th, 20th, 25th, 30th, and 40th percentiles of our data respectively,
each of them gives us a negative and significant relationship between downstream competition and
upstream innovation. Next, we use the 90th, 85th, 80th, 75th, 70th, and 60th percentiles of our
sample to run the regression respectively, finding that downstream competition is positively related to
upstream innovation with all of these subsamples. Taken together, the above results based on sample
splitting provide support for the U-shaped relationship existing between downstream competition and
upstream innovation. (3) Finally, we add a cubic term of downstream industry competition into our
model specification to test if the nonlinear relationship is S-shaped rather than U-shaped. We find out
that the coefficient estimates on downstream competition become insignificant with the cubic term
added in the model, and the model goodness of fit has only been improved by 0.0002. Thus, it is
unlikely that downstream competition has a S-shaped relationship with upstream innovation. The
model with a quadratic term works better for our data.
Second, our main dependent variable, citation-weighted patent counts, is constructed based on
weighting firms’ patent counts by their citations. The concern is that patent quality might be sensitive
to a specific weighting technique (Aghion et al., 2013). To address this concern, we use citations per
patent and total citations as alternative proxies for patent quality in the regressions as well. We apply
three different models in our regression: Negative Binomial, OLS, and Poisson models. Both in the
case of citations per patent and in the case of total patent citations, our results provide support for a
U-shaped relationship between downstream competition and upstream innovation.
Third, we re-run our regressions by using sample period 1976 - 2001 to address the concern that
patent citations close to the end of sample year would be biased. Though NBER updates the data
until 2006, some patents applied for after 2001 may not have been granted due to significant grant
lags in some technology areas. Furthermore, most patents require a significant number of years to
reach their full citation potential. By allowing five years from the date of application, we attempt to
minimize these problems. We again run negative binomial, poisson and OLS regression models, and
as in the baseline model, the U-shaped relationship between downstream competition and upstream
innovation is highly significant.
Fourth, our finding of a U-shaped relationship between downstream competition and upstream
innovation differs from the work of Aghion et al. (2005), which finds an inverted-U relationship
between horizontal industry competition and innovation. The concern is that this difference may be
driven by different industries in the samples of these two studies. To address this concern, we re-run
our regressions using the same sample industries covered by Aghion et al. (2005), i.e. four-digit SIC
from 2000 to 3999, using negative binomial, Poisson and OLS regression models.
Finally, in Section 5.2 we define a competitive shock for a downstream industry by whether the
44
largest tariff rate reduction in the downstream industry is three times larger than the median tariff
rate reduction in that industry. Alternatively, we also try two other definitions of the competitive
shock for a downstream industry. Specifically, we define the competitive shock by whether the largest
tariff rate reduction is larger than two times, or one and a half, the median tariff rate reduction. Our
results are robust to these two different definitions of competitive shock.
Overall, the results provide support for a U-shaped relationship between competition and innova-
tion.
B Appendix: Proofs
B.1 Proof of Lemma 1
Using (4), we can express (7) as follows:
−2[−1
3
(12 −
∆∗Mθ6
)− θ
6
(1θ −
∆∗M3
)]= ∆∗M ; or
23 −
2∆∗Mθ9 = ∆∗M ;
which yields ∆∗M = 6/ (9 + 2θ).
Note that our parametric restriction θ ∈ Θ with Θ = (0, 9/2) ensures that the second-order
condition, 2θ9 < 1, is satisfied. Note also that at ∆∗M , the smallest expected demand and price-cost
margin a Firm i can expect to obtain (in the no-access case) simplify to di = 12 −
∆∗Mθ6 = 1
2 −θ
(9+2θ)
and Pi = 1θ −
∆∗M3 = 1
θ −2
(9+2θ) , respectively; which are both strictly positive for all θ ∈ Θ.
Using (4) and substituting ∆∗M = 6/ (9 + 2θ) into expressions (5) and (6), we obtain z1M = z2M =2(9+θ)
(9+2θ)2 and Z∗M = 2(9+2θ) − h, respectively. �
B.2 Proof of Lemma 2
Using (4), we can express (10) as follows:
13
(12 +
∆∗T θ6
)+ θ
6
(1θ +
∆∗T3
)= ∆∗T ; or
13 +
∆∗T θ9 = ∆∗T ;
which yields ∆∗T = 3/ (9− θ).Note that our parametric restriction θ ∈ Θ with Θ = (0, 9/2) ensures that the second-order
condition, θ9 < 1, is satisfied. Note also that at ∆∗T , the smallest expected demand and price-cost
margin a Firm i can expect to obtain (in the no-access case) simplify to di = 12 −
∆∗T θ6 = 1
2 −θ
2(9−θ)
and Pi = 1θ −
∆∗T3 = 1
θ −1
(9−θ) , respectively; which are both strictly positive for all θ ∈ Θ.
Using (4) and substituting ∆∗T = 3/ (9− θ) into expressions (8) and (9), we obtain z∗1T = 18−θ2(9−θ)2 ,
and Z∗T = 118−2θ , respectively. �
B.3 Proof of Proposition 2
Recall from Lemmas 1 and 2 that Z∗M = 2(9+2θ)−h and Z∗T = 1
18−2θ . It then follows that limθ→0
Z∗T−Z∗M =
−1/6 + h and that limθ→9/2
Z∗T − Z∗M = h, and together with Proposition 1, this implies that:
• If h ∈ (0, 1/6) - there exists a threshold level of competition θ∗ (h) ∈ Θ such that the innovator
chooses market-wide licensing for all θ ∈ (0, θ∗ (h)), and chooses targeted licensing for all θ ∈
45
[θ∗, 9/2).
• If h is high - h ≥ 1/6 - targeted licensing is the optimal choice for the innovator for all θ ∈ Θ.
To see that ∂θ∗ (h) /∂h < 0, note that θ∗ (h) is the value of θ such that Z∗T − Z∗M = 0, or
A = 118−2θ∗ −
2(9+2θ∗) + h = 0. The implicit function theorem then yields ∂θ∗
∂h = − ∂A/∂h∂A/∂θ∗ < 0. �
C Appendix: Model Extensions
C.1 Revisiting the Tradeoff Between Market-Wide and Targeted Licensing
In the main analysis we have shown that competition increases the appeal of targeted licensing relative
to market-wide licensing, and hence that as competition intensifies, the innovator may switch from
the latter to the former. In this section, we explore further the licensing tradeoff and how it is affected
by competition.
At date 0, the innovator decides which type of licensing to opt for. She chooses market-wide
licensing24 over targeted licensing iff Z∗M ≥ Z∗T , iff:
2∑i=1
ziM (∆M , θ)−KM (∆M ) > z1T (∆T , θ)−KT (∆T ) . (18)
Re-writing expression (18) in the following way helps highlight the three key factors affecting the
tradeoff between market-wide licensing and targeted licensing:
[z2M (∆M , θ)]− [(z1T (∆M , θ)−KT (∆M ))− z1M (∆M , θ)−KM (∆M )]− [(z1T (∆T , θ)−KT (∆T ))− (z1T (∆M , θ)−KT (∆M ))] > 0.
(19)
The first square-bracketed factor captures the revenue advantage of market-wide licensing, i.e. the
extra revenue obtained from licensing to the second firm in the downstream market.
The second square-bracketed factor captures the dissipation disadvantage of market-wide licensing.
For a given innovation ∆M (produced at cost KT (∆M ) under targeted licensing and at cost KM (∆M )
under market-wide licensing) licensed to downstream Firm 1, the symmetric profits for Firm 1 under
market-wide licensing is smaller than the leader profits for that firm under targeted licensing; because
as discussed above Firm 1 is at a cost disadvantage in the former case and at a cost advantage in
the latter case. Accordingly, for a given innovation ∆M , the license fee extracted under market-wide
licensing is lower than the license fee extracted under targeted licensing.
Finally, the third square-bracketed factor captures the innovation disadvantage of market-wide
licensing. It represents the part of the difference between the two types of licensing that comes from
different innovation investments being made. As highlighted in Lemmas 1 and 2 equilibrium innovation
could be greater or lower under market-wide licensing than under targeted licensing, and hence this
disadvantage could be positive or negative.
As shown in Section 3.1, competition reduces the revenue advantage of market-wide licensing and
increases its dissipation disadvantage.25 Moreover, we know from Proposition 3 that competition in-
creases ∆T and reduces ∆M ; thus competition increases the innovation disadvantage. This is another
24Since innovation levels and license fees are identical for firms 1 and 2, we express the licensor’s payoff as twice thepayoff from firm 1 for simplicity.
25The discussion of Proposition 1 in Section 3.1 yields two points of relevance here: 1) the innovator’s payoff frommarket-wide licensing decreases with competition; and 2) the innovator’s payoff from targeted licensing increases withcompetition. Point 1) implies that the revenue advantage decreases with competition. Points 1) and 2) together implythat the dissipation disadvantage increases with competition.
46
way to express the positive impact of competition on the appeal of targeted licensing relative to
market-wide licensing stated in Proposition 1.
The revenue advantage and the dissipation disadvantage of market-wide licensing are closely re-
lated to the revenue effect and rent dissipation effect, respectively, identified in Arora and Fosfuri’s
(2003) insider-patentee paper. In their model, each incumbent competes in a differentiated downstream
product market where, similar to our model competition is captured by the degree of substitutability
between products. Each incumbent decides how many licenses to issue to potential new entrants,
anticipating that the licensee will enter the market with a product identical to that of the incum-
bent licensor. Issuing one more license generates additional revenue (revenue effect), but reduces the
incumbent’s profits (rent dissipation effect)26 by adding a direct competitor in the downstream market.
Despite highlighting two similar factors in the licensing tradeoff, Arora and Fosfuri’s (2003) model
differs from ours along critical dimensions. First, while as in our model competition reduces the revenue
effect; in contrast to our model it also reduces the rent dissipation effect, because the negative impact
of the licensee’s market entry is now spread more easily across all incumbents. In their model, the
second effect dominates, and hence competition leads to more licensing, not less. Second, unlike our
model of endogenous innovation, their setup considers firms’ licensing strategy for a given, exogenously
determined innovation level. This exogeneity precludes any analysis of the innovation disadvantage of
market-wide licensing discussed above, or of the central research question of this paper, namely the
subtle connection between competition, licensing, and innovation.
C.2 Auction Contract
In the main model we assume that transaction costs associated with auctions are prohibitively high,
making them difficult to implement. In this section we relax this assumption and discuss the results
of our model in the context of an auction setup, and show that similar results can be obtained.
Consider the case of targeted licensing, and suppose that the innovator auctions one license.
For a given innovation ∆Ta to be licensed to the winner of the auction, the equilibrium auction
bid by Firm i is very similar to - though distinct from - the equilibrium license fee in the main
model:27 ziTa (∆Ta, 0, θ) = πi (∆Ta, 0, θ) − πi (0,∆Ta, θ). The only difference is that in the main
model the innovator commits to sell on Firm 1 only, and hence Firm 1’s symmetric profit (i.e. if
it does not get the innovation) is π1 (0, 0, θ); while here each downstream firm conjectures that if it
does not get the innovation the rival firm will get it, and hence the symmetric profit for Firm i is
πi (0,∆Ta, θ). Using ziTa (∆Ta, 0, θ) and expression (4), one can readily show that: Under targeted
licensing in an auction setup, a unique equilibrium exists, in which the innovator chooses innova-
tion levels ∆∗Ta = 2/3. This in turn implies - assuming Firm 1 wins the auction - downstream
price-cost margins P1 (∆∗Ta, 0, θ) =[
1θ + 2
9
]and P2 (0,∆∗Ta, θ) =
[1θ −
29
]; and expected demands
d1 (∆∗Ta, 0, θ) =[
12 + θ
9
]and d2 (0,∆∗Ta, θ) =
[12 −
θ9
]. Equilibrium auction bid, and payoff to the
innovator, simplify to z∗1Ta = 4/9, and Z∗Ta = 2/9, respectively.
Under market-wide licensing, auctioning two licenses to the two downstream firms yields the trivial
result that both firms would bid the reservation price set by the innovator, and hence the problem
reverts to the problem examined above. For a given innovations ∆Ma to be licensed to downstream
firms i and j, the equilibrium price received by the innovator is exactly the same as the optimal license
fee charged to Firm i in the main model: ziMa (∆Ma,∆Ma, θ) = πi (∆Ma,∆Ma, θ) − πi (0,∆Ma, θ).
Thus under market-wide licensing the outcome is identical to the outcome in the main model, which is
stated in Lemma 1, and which we repeat here for convenience. Under market-wide licensing, a unique
26The dissipation effect also plays a key role in Arora et al.’s (2012) recent work on the tradeoff between decentralizedlicensing - where the business unit has authority over licensing decisions - and centralized licensing in a specializedlicensing unit. As well, see related work by Fosfuri (2006).
27We add subscript a to remind the reader that we are examining the auction case.
47
equilibrium exists, in which the innovator chooses innovation levels ∆∗Ma = ∆∗M = 69+2θ . This in turn
implies downstream price-cost margins P1 (∆∗Ma,∆∗Ma, θ) = P2 (∆∗Ma,∆
∗Ma, θ) = 1/θ; and expected
demands d1 (∆∗Ma,∆∗Ma, θ) = d2 (∆∗Ma,∆
∗Ma, θ) = 1/2. License fees, and payoff to the innovator,
simplify to z∗1Ma = z∗2Ma = 2(9+θ)
(9+2θ)2 , and Z∗Ma = 2(9+2θ) − h, respectively.
One can see that while equilibrium innovation and innovator payoff are now independent of com-
petition under targeted licensing in the auction case, the key results are still similar to those of the
main model. In particular, competition continues to increase the appeal of targeted licensing over
market-wide licensing (∂ (Z∗Ta − Z∗Ma) /∂θ > 0). Overall, from the foregoing analysis one can derive
results equivalent to Proposition 4 in the context of an auction. In an auction setup, if the exoge-
nous (relative) cost of market-wide licensing h is moderately negative - h ∈ (−1/9, 0) - there exists a
threshold level of competition θ∗a (h) ∈ Θ such that the innovator chooses market-wide licensing for all
θ ∈ (0, θ∗a (h)), and chooses targeted licensing for all θ ∈ [θ∗a, 9/2). If h is positive - h ≥ 0 - targeted
licensing is the optimal choice for the innovator for all θ ∈ Θ. And if h very negative - h ≤ −1/9 -
market-wide licensing is the optimal choice for the innovator for all θ ∈ Θ.
C.3 Licensing Contract With A Fixed Fee Plus Royalty
In the main model we assume that the licensing contract is based on fixed fee. In this section we relax
this assumption and discuss the results of our model in the context of the licensing contract based on
both royalty and fixed fee.
Targeted Licensing. Suppose that the innovator plans to license her innovation to Firm 1 only.
In addition of charging a fixed licensing fee, the innovator imposes royalties in the licensing deal as
well. We derive the equilibrium by backward induction.
At date 3, price competition takes place between firms 1 and 2. Two firms choose prices to maximize
their expected payoff, taking costs and innovations as given:
maxp1
π1 (∆T , p1, p2, θ, r) = maxp1
(p1 − c+ ∆T − r) d1 (p1, p2, θ) ,
maxp2
π2 (p2, p1, θ) = maxp2
(p2 − c) d2 (p1, p2, θ) ,
where r is the per unit royalty, and the expected demand d1 (p1, p2, θ) and d2 (p1, p2, θ) are defined
as in (1). Taking the FOCs with respect to price, and solving the resulting system of two equations
yields the following equilibrium profits:
π1 (∆T , θ, r) =
[1
θ+
∆T − r3
] [1
2+
(∆T − r)θ6
],
π2 (∆T , θ, r) =
[1
θ− ∆T − r
3
] [1
2− (∆T − r)θ
6
].
At date 2, as can readily be shown, in equilibrium Firm 1 licenses innovation ∆T from the innovator
if and only if (iff) the payoff it can obtain if she buys the license is at least as large as its payoff if it
does not buy the license: π1 (∆T , θ, r)− zT (∆T , θ, r) ≥ π1 (0, θ, r).
At date 1, the foresighted innovator sets the highest license fee zT that she can extract from Firm
1, subject to her buying the license, which is simply:
zT (∆T , θ, r) = π1 (∆T , θ, r)− zT (∆T , θ, r) =
[1
θ+
∆T − r3
] [1
2+
(∆T − r)θ6
]− 1
2θ.
48
The innovator chooses innovation ∆∗T to maximize the following payoff:
ZT = zT (∆T , θ, r) + r · d1 (p1, p2, θ)−KT (∆T ) ,
with the expected demand d1 (p1, p2, θ) = 12 + (∆T−r)θ
6 . Using expression (7), and taking the FOC
with respect to ∆T and r, yields the optimal innovation, royalty, and payoff for the innovator are:
∆∗T =3
8− θ,
r∗T =6
θ(8− θ),
Z∗T =θ + 1
2θ(8− θ).
Under the targeted licensing with a fixed fee plus royalty contract, the licensee, Firm 1, will need
to pay a per unit royalty in addition to a fixed fee. As in the main model, the optimal fixed fee is the
difference between Firm 1’s access profits and no-access profits. The only difference here is that in the
profit maximization for Firm 1, she has to pay a per unit royalty, r. The equilibrium innovation level
that the innovator chooses is ∆∗T = 38−θ , which clearly suggests a similar relationship as in the main
model - innovation ∆∗T is increasing in downstream competition, θ.
Market-Wide Licensing. Suppose now the innovator plans to license innovations to both down-
stream firms. In addition of charging a fixed licensing fee, the innovator imposes royalties in the
licensing deal as well. We derive the equilibrium by backward induction.
At date 3, price competition takes place between firms 1 and 2. Specifically, Firm i, i = 1, 2,
chooses pi to maximize its expected payoff, taking costs and innovations as given:
maxpiπi (∆i, pi, pj , θ, r) = max
pi(pi − c+ ∆M − r) di (pi, pj , θ) ,
with a similar deriving procedure as before, Firm i’s expected profits simplify to πi (∆iM ,∆jM , θ) =
1/ (2θ).
At date 2, as can readily be shown, in equilibrium Firm i licenses innovation ∆M from the innovator
if and only if (iff) the payoff it can obtain if she buys the license is at least as large as its payoff if it
does not buy the license: πi (∆i,∆j , θ)− ziM (∆i,∆j , θ) ≥ πi (0,∆j , θ), with ∆i = ∆j = ∆M .
At date 1, the foresighted innovator sets the highest license fee ziM that she can extract from Firm
i, subject to both firms buying the license, which is simply:
ziM (∆M , θ) = πi (∆M ,∆M , θ)− πi (0,∆M , θ) =1
2θ−[
1
θ− ∆M − r
3
] [1
2− (∆M − r)θ
6
].
The innovator chooses innovation ∆∗M to maximize the following payoff:
ZM = r · d1 (p1, p2, θ) + r · d2 (p1, p2, θ) + z1M (∆M , θ) + z2M (∆M , θ)−KM (∆M ) .
Using expression (7), and taking the FOC with respect to ∆M and r respectively, we obtain the
following equilibrium results:
∆∗M = 1,
r∗T = 1 +3
2θ,
49
Z∗M =1
2+
1
4θ.
Under market-wide licensing and a contract with a fixed fee plus royalty, a unique equilibrium
exists, in which the innovator chooses innovation levels ∆∗M = 1, and the payoff to the innovator,
simplifies to Z∗M = 12 + 1
4θ . The equilibrium innovation level is now constant, and the equilibrium
licensing fee for the innovator is decreasing in downstream competition level, θ. One can see that while
equilibrium innovation is now independent of competition under market-wide licensing, the key results
are still similar to those of the main model.
Targeted Licensing vs. Marketed-wide Licensing. We proceed to compare the payoffs
under targeted licensing and marketed-wide licensing as follows:
∆Z = Z∗T − Z∗M =θ + 1
2θ(8− θ)− (
1
2+
1
4θ).
Let ∆Z = 0, clearly there is a threshold point of θ, θ∗ = 6.9, such that above this point, the targeted
licensing dominates the market-wide licensing, i.e., ∆Z ≥ 0; while below this point, the market-wide
licensing becomes optimal, i.e., ∆Z > 0. Together with the above results under targeted and market-
wide licensing, one can easily deduce that the equilibrium innovation has a U-shaped relationship with
downstream competition. These key results under a fixed fee plus royal contract are equivalent to
those in our main model where a fixed fee contract is applied. In particular, competition continues to
increase the appeal of targeted licensing over market-wide licensing (∂ (∆Z) /∂θ > 0). Overall, in the
context of a fixed fee plus royalty contract, there exists a threshold level of competition θ∗, θ∗ = 6.9,
such that the innovator chooses market-wide licensing for all θ ∈ (0, 6.9), and chooses targeted licensing
for all θ ∈ [6.9, 8). This further points to a U-shaped relationship between downstream competition
and upstream innovation.
50
h
9
2𝜃∗
ℎ −1
6
𝑎) ℎ ∈ (0, ൗ1 6)
Market − WideLicensing
Targeted
Licensing
𝑍𝑇∗ − 𝑍𝑀
∗
𝜃
h
9
2
𝜃
ℎ −1
6
b) ℎ ≥ Τ1 6
𝑍𝑇∗ − 𝑍𝑀
∗
Targeted
Licensing
Figure 1: Product Market Competition and Licensing Strategy
∆∗
9
2
𝜃
1
3
a1) ℎ ∈ (0, Τ1 6) , 𝜃∗ (ℎ) ≥
9
4
2
3
𝜃∗9
4
9
2
𝜃
1
3
∆∗
2
3
𝜃∗ 9
4
a2) ℎ ∈ (0, Τ1 6) , 𝜃∗ (ℎ) < Τ9 4
9
2
𝜃
b) ℎ ≥ Τ1 6
∆∗
Figure 2: Product Market Competition and Innovation